SOLUTION: The rectangular floor of a closet is divided into two right triangles by drawing a diagonal. One leg of the right triangle is 10 feet less than twice than twice the other leg. The

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The rectangular floor of a closet is divided into two right triangles by drawing a diagonal. One leg of the right triangle is 10 feet less than twice than twice the other leg. The       Log On


   



Question 1134641: The rectangular floor of a closet is divided into two right triangles by drawing a diagonal. One leg of the right triangle is 10 feet less than twice than twice the other leg. The hypotenuse is 25 feet. Determine the​ closet's length and width. Let the width be the shorter side.
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52793) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let w be the width.  Then the length is  (2w - 10).


Your equation to find "w" is


w^2 + (2w-10)^2 = 25^2.


Simplify and solve for w.


Then evaluate 2w-10 as the length.


Happy calculations !


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The rectangular floor of a closet is divided into two right triangles by drawing a diagonal.
One leg of the right triangle is 10 feet less than twice the other leg.



Let w be the width. Then the length is +%282w+-+10%29.
Your equation to find "w" is
w%5E2+%2B+%282w-10%29%5E2+=+25

5w%5E2+-+40+w+%2B+100+=+625.....simplify
w%5E2+-+8+w+%2B+20+=+125
w%5E2+-+8+w+%2B+20+-125=0
w%5E2+-+8+w++-105=0...factor
%28w+-+15%29+%28w+%2B+7%29+=+0
w=15
w=-7-> disregard negative solution


find the other leg = 2w-10:
2w-10=2%2A15-10=20
the​ closet's length is 20 ft and width is 15 ft