SOLUTION: The area fo a rectangle is 66ft squared and the diagonal of the rectangle is square root of 157 ft. What are the dimensions of the rectangle.

Question 201094: The area fo a rectangle is 66ft squared and the diagonal of the rectangle is square root of 157 ft. What are the dimensions of the rectangle.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The area fo a rectangle is 66ft squared and the diagonal of the rectangle is square root of 157 ft. What are the dimensions of the rectangle.
.
Let x = width
and y = length
.
Since we have two unknowns, we'll need two equations:
Equation 1:
xy = 66
Equation 2:

x^2 + y^2 = 157
.
Solving equation 1 for y:
y = 66/x
Substituting the above into equation 2 we can solve for x:
x^2 + y^2 = 157
x^2 + (66/x)^2 = 157
x^2 + 4356/x^2 = 157
x^4 + 4356 = 157x^2
x^4 - 157x^2 + 4356 = 0
Factoring we get:
(x^2-121)(x^2-36) = 0
x = {11,6}
.
Dimensions of rectangle are 11 feet by 6 feet
RELATED QUESTIONS
the length of a rectangle is one more than twice its width. The area is 66ft squared/ how (answered by addingup)

The perimeter of a rectangle is 16, and its diagonal is square root of 40. Find its... (answered by Photonjohn)

The area of a rectangle is 63 ft squared. the length is 2 ft longer than the width.... (answered by drk)

what are the sides of a rectangle whose area is 448 ft squared? one side is x+2 ft and... (answered by Fombitz)

The perimeter of a rectangle is 34 ft. and the diagonal is 13 ft. What are the length and (answered by mananth)

What is the diagonal of a 20 ft wide and 24 ft long rectangle? (answered by Alan3354)

if the area of a rectangle is 7200 ft squared and the length is 120 ft what is the length (answered by ewatrrr)

If a rectangle has an area of 144ft squared, its length is 18 ft, and the width is 8 ft.... (answered by Alan3354,mananth)

A rectangle is 6ft long and 11 ft wide. What is the length of the diagonal of the... (answered by Alan3354)