Question

A 15-ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 3 ft longer than the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.

Answer 1

the horizontal distance ----> x
the height -----> y

The horizontal distance is 3 ft longer than the height -----> x = y + 3

Lets apply the Pythagorean Theorem:

15^2 = x^2 + y^2

225 = x^2 + (x - 3)^2

225 = x^2 + (x^2 - 6x + 9)

225 = 2x^2 - 6x + 9

0 = 2x^2 - 6x + 9 - 225

0 = 2x^2 - 6x - 216 ----> divide all by 2

0 = x^2 - 3x - 108 -----> FOIL

0 = (x - 12)(x + 9)

x = 12 ( true ) . . .. x = -9 ( impossible negative numbers in length )

x = y + 3 ----> when x = 12. . .. . .. it implies y = 9

Answer 2

ok @sharron482

Answer 3

ok

Answer 4

yaa

Answer 5

am i right? @ajprincess

Answer 6

am i right? @ganeshie8

Answer 7

Yeah