A triangular arch is to be constructed over a busy street in order to place a sky bridge traversing one side of the triangle to the other. The base of the arch spans the width of the street, which is 20 feet. Each side of the triangular arch measures 30 feet in length. If the entrances of the sky bridge lie at the midpoints of each side of the triangular arch, and the bridge is to be parallel to the street below, how long will the sky bridge be?

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

7 is the median   7.875 is the mean

step-by-step explanation:

3,4,5,6,8,11,13,13

mr. india