Question

An engineer is designing a new dam for a river. The retaining wall of the dam will be angled such that the height above the ground of the top at the wall is three times the horizontal distance between where it begins and where it ends at ground level. The outer angled wall will be 100-feet long. This relationship is shown below.
Which system of equations can be used to determine y, the height above the ground at the top of the wall, and x, the horizontal distance between where the wall begins and where it ends at ground level.

Recall the Pythagorean theorem, a2 + b2 = c2, where a and b are the side lengths of a right triangle, and c is the length of the hypotenuse.

Answer 1

Let y = 3x

use pythagorean

100^2 = x^2 + 3x*3x =  x^2 + 9x^2 = 10x^2
solve for x

10000 = 10x^2 ; x^2 = 10000/10 = 1000

x = sqrt(1000) = 31.623 ft

y = 31.623*3 = 94.87ft

Answer 2

By the Pythagorean theorem we have:
 x ^ 2 + y ^ 2 = 100 ^ 2
 Then, we have:
 "the height above the ground of the top at the wall is three times the horizontal distance between where it begins and where it ends at the ground level"
 y = 3x
 Answer:
 The system of equations is:
 x ^ 2 + y ^ 2 = 100 ^ 2
 y = 3x