The diagonal of a rectangular pen is 40 feet. The width of the pen is 7 feet less than the length. Find the length of the pen.

Question

The diagonal of a rectangular pen is 40 feet. The width of the pen is 7 feet less than the length. Find the length of the pen. How long is the pen in feet?

Answer 1

I am not sure that the problem is entered in here correctly.

IF you let the width be 8 less than the length, then you get a nice, whole number answer.

I will solve it using the Width (W) is 8 less than the Length (L) and the diagonal is 40 ft.

Using the Pythagorean Theorem, this right triangle will be L² + W² = 40²

Subsitutuing W = L-8, this becomes L² - (L-8)²= 1600

(L-8)²= L² -16L + 64

Now our Pythag Thm equation is

L² + L² - 16L + 64 = 1600

Putting everything on the left side,

2L² - 16L -1536 = 0

Divide everything by 2, and get

L² - 8L - 768 = 0

(L - 32) (L + 24) = 0

So L=32 feet or L = - 24 feet, so L = 32 feet is the correct answer.

Checking: L=32, W= 24 (32 - 8 = 24) and L² + W² = 32² + 24² = 1600 = 40² It is correct.