The area of a rectangle is 75 square centimeters and its perimeter is 40 centimeters. Find the dimensions of the rectangle.
A) 13 cm by 2 cm
B) 24 cm by 5 cm
C) 16 cm by 3 cm
D) 15 cm by 5 cm

Question

Quizplus · Accepted Answer

Let the length of the rectangle be x cm and the width be y cm.
Given, xy = 75 and 2(x+y) = 40, which simplifies to x+y=20.
Using these two equations, we can solve for the values of x and y.
One way to do this is to substitute y = 20 - x from the second equation into the first equation:
x(20-x) = 75
20x - x^2 = 75
Rearranging and solving for x:
x^2 - 20x + 75 = 0
(x-15)(x-5) = 0
So, x = 15 or x = 5.
If x = 15, then y = 20 - x = 5, which does not satisfy xy = 75.
If x = 5, then y = 20 - x = 15, which does satisfy xy = 75.
Therefore, the dimensions of the rectangle are 5 cm by 15 cm, and the answer is D.

The Area of a Rectangle Is 75 Square Centimeters and Its