Problem: the two lines y = x and x = - 5 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length of a cube whose surface area is equal to 6 z ?
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 5 , - 5 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 × 4 ) = 25 / 2 ; so z = 25 / 2 . the next step requires us to find the length of a side of a cube that has a face area equal to 25 / 2 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 25 / 2 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 25 / 2 . clearly s = √ 25 / 2 = 5 / √ 2 , oranswer choice ( b ) ."
annotated_formula: sqrt(divide(multiply(5, 5), const_2))