SOLUTION: A rectangle is three times as long as it is wide and has the same perimeter as a square whose area is 100 square feet larger than that of the rectangle. What are the dimensions of

Algebra ->  Rectangles -> SOLUTION: A rectangle is three times as long as it is wide and has the same perimeter as a square whose area is 100 square feet larger than that of the rectangle. What are the dimensions of       Log On


   

Question 1107891: A rectangle is three times as long as it is wide and has the same perimeter as a square whose area is 100 square feet larger than that of the rectangle. What are the dimensions of both the rectangle and the square?
Found 2 solutions by josgarithmetic, TeachMath:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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A rectangle is three times as long as it is wide and has the same perimeter as a square whose area is 100 square feet larger than that of the rectangle. What are the dimensions of both the rectangle and the square?
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RECTANGLE
Dimensions w for width and 3w for length
Perimeter Expression: 6w%2B2w=8w
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Area Expression: 3w%5E2

The SQUARE
Side Length x
Perimeter: 4x
Area: x^2
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Translate the description: whose area is 100 square feet larger than that of the rectangle:
x%5E2=3w%5E2%2B100
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Also symbolize the first part, Rectangle has the same perimeter as a square whose area :
8w=4x


The system of equations: system%28x%5E2=3w%5E2%2B100%2C8w=4x%29, and should be solvable...,
Note, 2w=x can be a good substitution to use as first step.
highlight_green%28%282w%29%5E2=3w%5E2%2B100%29
.
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Answer by TeachMath(96) About Me  (Show Source):
You can put this solution on YOUR website!
width of rectangle = 40/8, or 5 ft
Length of rectangle: 3(5), or 15 ft
One side of square: sqrt(100) = 10 ft