SOLUTION: The combined area of square and a rectangle is 57 square feet. The width of a rectangle is 3 feet more than the length of a side of the square, and the length of the rectangle is 5

Question 1004416: The combined area of square and a rectangle is 57 square feet. The width of a rectangle is 3 feet more than the length of a side of the square, and the length of the rectangle is 5 feet more than the length of a side of the square. Find the length of the rectangle.
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
Side of the square: x
Rectangle width and length:
width = 3 + x
length = 5 + x
--------------------
Area of square: x^2
area of rectangle: (3 + x)(5 + x)
--------------------
Add the area of the square and the rectangle:
x^2 + (3+x)(5+x) = 57 factor (FOIL) and you get:
x^2 + (15 + 8x + x^2) = 57 Add x^2 on left and subtract 15 on both sides:
2x^2 + 8x = 42 Divide both sides by 2:
x^2 + 4x= 21 Subtract 21 on both sides:
x^2 + 4x - 21 = 0 Factor this equation: you need to find factors of 21 that when added or subtracted will give you 4: 21 is divisible by 1, 3, 7, 21 We have our numbers, 7-3 = 4 and 7*-3= -21:
(x + 7)(x - 3) = 0 Split into 2 equations:
x+7= 0 or x-3= 0
x= -7 or x= 3 Eliminate -7 and you get:
x = 3 This is the side of the square
The rectangle:
Width: 3+3= 6
Length: 3+5= 8
Proof, Add areas:
Square: 3^2= 9
Rectangle: 6*8= 48
9+48= 57 We have the correct answer
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