Solve.
-The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 160 square centimeters. Find the side of the
Square.
A)10 cm
B)64 cm
C)8 cm
D)2 cm

Question

Quizplus · Accepted Answer

Let x be the length of the rectangle, then its width is x + 4. The area of the rectangle is length x width, which equals x(x + 4) = x^2 + 4x square meters.

The area of the square is x^2 square meters.

The sum of the areas of the square and the rectangle is 160 square centimeters, or 0.016 square meters.

So, we have the equation x^2 + 4x + x^2 = 0.016

Simplifying this equation gives us 2x^2 + 4x - 0.016 = 0

Solving for x using the quadratic formula, we get x ≈ 3.975 or x ≈ -4.987

Since the length of the rectangle cannot be negative, we take x ≈ 3.975.

Therefore, the side of the square is x = 3.975 ≈ 8 cm (rounded to the nearest cm).

So, the best choice is C)8 cm. Let x be the length of the rectangle.
Then, the width is x + 4.
The area of the square is x^2.
The area of the rectangle is x(x+4) = x^2+4x.
The sum of the areas is x^2+x^2+4x=2x^2+4x.
2x^2+4x=160
x^2+2x=80
x^2+2x-80=0
(x+10)(x-8)=0
Since the length of a rectangle cannot be negative, we have x=8.
Therefore, the side of the square is also 8 cm.
Thus, the answer is C) 8 cm.

Solve. -The Side of a Square Equals the Length of a a Rectangle