Problem: Article: The formula is D=w2+l2{\displaystyle D={\sqrt {w^{2}+l^{2}}}}, where D{\displaystyle D} equals the length of the rectangle's diagonal, l{\displaystyle l} equals the length of the rectangle, and w{\displaystyle w} equals the width of the rectangle. This method will only work if you are given the length of the diagonal and the length of the side of the rectangle. You might also see the formula written as D=w2+h2{\displaystyle D={\sqrt {w^{2}+h^{2}}}}, where h{\displaystyle h} equals the height of the rectangle and is used instead of length. The variables l{\displaystyle l} and h{\displaystyle h} refer to the same measurement. Make sure you substitute for the correct variables. For example, if you are trying to find the width of a rectangle that has a diagonal length of 5 centimeters, and a side length of 4 centimeters, your formula will look like this: 5=w2+42{\displaystyle 5={\sqrt {w^{2}+4^{2}}}} You need to do this to get rid of the square root sign, which makes isolating the width variable easier. For example:5=w2+42{\displaystyle 5={\sqrt {w^{2}+4^{2}}}}52=w2+42{\displaystyle 5^{2}=w^{2}+4^{2}}25=w2+16{\displaystyle 25=w^{2}+16} To do this, you need to subtract the squared length from each side of the equation. For example, in the equation 25=16+w2{\displaystyle 25=16+w^{2}}, you would subtract 16 from each side.25=16+w2{\displaystyle 25=16+w^{2}}9=w2{\displaystyle 9=w^{2}} To do this, you need to find the square root of each side of the equation. For example:9=w2{\displaystyle {\sqrt {9}}={\sqrt {w^{2}}}}3=w{\displaystyle 3=w} Don't forget to include the unit of measurement. For example, for a rectangle with a diagonal length of 5cm{\displaystyle 5cm} and a side length of 4cm{\displaystyle 4cm}, the width would be 3cm{\displaystyle 3cm}.
Summary: Set up the formula for the diagonal of a rectangle. Plug the values for the diagonal and side length into the formula. Square both sides of the formula. Isolate the w{\displaystyle w} variable. Solve for w{\displaystyle w}. Write your final answer.

INPUT ARTICLE: Article: It's important to warm up your muscles before getting into the splits. Perform about 15 minutes of cardio to warm up your muscles. There are many options for cardio so do what you enjoy so you don't get bored by the repetition. Whether you enjoy jumping jacks, climbing stairs, or jogging, get your muscles to loosen up and slowly work them up to more vigorous movements. Increase the intensity of your warm up with jump rope, squats, or box jumps to get your blood flowing in your legs. Form a bridge by lying with your back on the floor and trying to push yourself up on your feet and hands. Your knees should be bent with your palms and feet planted on the ground. You should try to form a bridge by lifting your back as far from the ground as you can by pushing down through your feet and hands. Point your elbows to the ceiling and feel your back stretch. It may be difficult at first but with time and practice your flexibility will increase. Don't force anything if you start to feel pain. Push yourself to feel a stretch but don't push so far that you feel pain. Use the runner's stretch for your lower body. Get into the lunge position by taking a step forward. Bring your fingertips as low as you can. Raise your butt by slowly straightening your front leg. Inhale as you straighten your leg. Feel your front leg stretch and exhale. Get back into the starting lunge position and repeat. Repeat the runners stretch for both legs, repeating 4x per leg. Perform a standing side stretch by reaching over your head, grip your fingers together but extend your pointer fingers and keep them together. Stretch and inhale as you get as long as you can while bending to one side. Take a deep and slow breath as you hold your pose for 5 seconds then return to a tall, standing position with your arms above your head. Make sure to perform the standing side stretch on both sides of your body.

SUMMARY: Perform cardio exercises. Stretch your back. Stretch your lower body. Stretch your upper body.

In one sentence, describe what the following article is about: Fill a lawn roller full of water and walk it over the entire sod. This presses down the sod to ensure good root contact with the soil before watering. Keeping the grass moist during the first few weeks is essential. During this time, the grass roots are establishing and growing. Without plenty of water, this process will slow or halt, and the sod die before it takes. After the first two weeks, water the grass a few times a week to keep it from drying out. Use a sprinkler system to ensure the grass gets evenly watered. Don't wait until the grass looks brown to water it. Do a soil test by sticking your finger into the dirt. If the soil feels moist to a depth of several inches, it's fine. If the dirt feels dry on the surface or to a depth of an inch or two, it's time to water it. Shade-grown grass should be watered less frequently, since it holds dew longer. Water just to the point of puddling, then stop. If the sod lifts up off the soil, it has been overwatered. Mowing before the roots are well established can pull them out of the soil and damage your sod. Wait patiently until the grass is at least 3 inches (7.6cm) tall, and gently pull up on several areas of sod to confirm it is firmly attached. Once the lawn is ready, mow it down to no shorter than of its height, and never below 2 inches (5 cm). Always be sure the mower blades are sharp, straight and clean, Mow in a different directional pattern each time the grass is mowed to ensure even growth. You can bag the clippings, but leaving them on the lawn will actually improve its health, since they act as free fertilizer. Use the same starter fertilizer to dress the lawn after a month has passed. This is necessary to replace the nutrients that may have been washed away during a month of heavy watering. After the first month, you need only fertilize your grass once or twice a season to replace nutrients in the years to come. Keeping up with watering, mowing and fertilizing your lawn is the best way to grow thick, healthy grass, and it's also the best way to keep weeds away. Weeds tend to move in when the grass gets patchy. They're nature's way of covering up bare spots in the ground. If you make sure there aren't bare spots to begin with, you won't have to worry much about weeds. If you notice an area where the sod seems to be dead, replace it as soon as possible. Tear up the old sod, enrich the soil underneath with compost, and add fresh sod, making sure the seams lay right next to the healthy grass on either side. This will prevent weeds from coming up where the sod is dead.
Summary:
Walk over the lawn with a lawn roller. Water it thoroughly for the first two weeks. Mow once the grass is at least 3 inches (7.6cm). Fertilize the lawn again after a month. Maintain your lawn to keep it free of weeds.