SOLUTION: The combined area of a square and a rectangle is 54 square meters. The length of the rectangle is 5 meters more than the length of a side of the square, and the width of the recta

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The combined area of a square and a rectangle is 54 square meters. The length of the rectangle is 5 meters more than the length of a side of the square, and the width of the recta      Log On


   

Question 1070617: The combined area of a square and a rectangle is 54 square meters. The length of the rectangle is 5 meters more than the length of a side of the square, and the width of the rectangle is 2 meters more than a side of the square. Find the length and width of the rectangle.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The combined area of a square and a rectangle is 54 square meters.
The length of the rectangle is 5 meters more than the length of a side of the square, and the width of the rectangle is 2 meters more than a side of the square.
Find the length and width of the rectangle.
:
let x = the side of the square
then
x^2 = the area of the square
The rectangle
(x+5) = the length of the rectangle
and
(x+2) = the width of the rectangle
then
(x+5)*(x+2) = x^2 + 7x + 10; the area of the rectangle
The sum of the square and the rectangle areas
x^2 + x^2 + 7x + 10 = 54
2x^2 + 7x + 10 - 54 = 0
a quadratic equation
2x^2 + 7x - 44 = 0
Use the quadratic formula to find x
I got a positive solution of x = 3.256 is the side of the square
The rectangle is 8.256 by 5.256
;
:
Check this on a calc: 3.256^2 + (8.256*5.256) =