SOLUTION: The combined area of a square and a rectangle is 151 square centimeters. The width of the rectangle is 4 centimeters more than the length of a side of the square, and the length of

Algebra ->  Rectangles -> SOLUTION: The combined area of a square and a rectangle is 151 square centimeters. The width of the rectangle is 4 centimeters more than the length of a side of the square, and the length of      Log On


   

Question 222983: The combined area of a square and a rectangle is 151 square centimeters. The width of the rectangle is 4 centimeters more than the length of a side of the square, and the length of the rectangle is 5 centimeters more than its width. Find the dimensions of the square and 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 151 square centimeters.
The width of the rectangle is 4 centimeters more than the length of a side of the square,
and the length of the rectangle is 5 centimeters more than its width.
Find the dimensions of the square and the rectangle.
:
Let x = side of the square
:
"The width of the rectangle is 4 centimeters more than the length of a side of the square,"
x + 4 = width of the rectangle
:
"the length of the rectangle is 5 centimeters more than its width."
(x+4) + 5 = length of the rectangle
which is (x+9)
:
Find the dimensions of the square and the rectangle.
:
Area of square + area of rectangle = 151 sq/cm
x*x + (x+4)(x+9) = 151
FOIL
x^2 + x^2 + 9x + 4x + 36 = 151
:
2x^2 + 13x + 36 - 151 = 0
:
2x^2 + 13x - 115 = 0; our old friend, the "quadratic equation"!
:
This will factor to:
(2x + 23)(x - 5) = 0
:
Positive solution is what we want here
x = 5 is the side of the square
then
5 + 4 = 9 cm width of the rectangle
and
9 + 5 = 14 cm length of the rectangle
;
:
Check solution by finding the total area
5^2 + 9*14 =
25 + 126 = 151