SOLUTION: The diagonal of a rectangle is 2 ft longer than its length and 5 feet longer than its width. What are the dimensions of the rectangle?

Question 107935: The diagonal of a rectangle is 2 ft longer than its length and 5 feet longer than its width. What are the dimensions of the rectangle?
Found 2 solutions by MathLover1, edjones:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
The diagonal of a rectangle is longer than its and longer than its .
What are the dimensions of the rectangle?
Since the divides rectangle into two , we will use in order to find the dimensions of the rectangle.
In algebraic terms, where is the hypotenuse ( in your case the ) while and are the legs of the triangle (in your case the and ).
given:
=>
=>

we will substitute it in:

We need only positive root

=>

=>
Check:

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
The diagonal divides the rectangle into 2 equal right triangles.
Let the diagonal=c and the 2 sides be a and b.
a=c-2, b=c-5
a^2+b^2=c^2
(c-2)^2+(c-5)^2=c^2
c^2-4c+4+c^2-10c+25=c^2
c^2-14c+29=0
c^2-14c =-29
c^2-14c+49=49-29 complete the square
(c-7)^2=20
c-7=+-sqrt(20)
c=7+-sqrt(5*4)
=7+-2sqrt(5)
Only 7+2sqrt(5) is the only correct answer for the diagonal. the other would lead to negative numbers for the sides of the rectangle.
The sides of the rectangle are:
5+2sqrt(5) and 2+2sqrt(5)
Ed
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