The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 28-inch flat-screen television than a square 25 -inch flat-screen television? Options:
A) 79.5
B) 89.3
C) 85.5
D) 75.4
E) 72.5

Rationale: if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 28 - inch flat - screen television the diagonal ( hypotenuse ) = 28 so , we can apply the pythagorean theorem to get x ² + x ² = 28 ² simplify : 2 x ² = 28 ² divide both sides by 2 to get : x ² = 28 ² / 2 since the area of the square = x ² , we can see that the area of this square is 28 ² / 2 square 25 - inch flat - screen television the diagonal ( hypotenuse ) = 25 so , we can apply the pythagorean theorem to get x ² + x ² = 25 ² simplify : 2 x ² = 25 ² divide both sides by 2 to get : x ² = 25 ² / 2 since the area of the square = x ² , we can see that the area of this square is 25 ² / 2 difference in areas = 28 ² / 2 - 25 ² / 2 = ( 28 ² - 25 ² ) / 2 = ( 784 - 625 ) / 2 = 159 / 2 = 79.5 a
Answer: A