The area of a rectangle is 24 square centimeters, and its perimeter is 20 centimeters.Find the dimensions of the rectangle.
A) $\quad 6 \mathrm {~cm}$ by $7 \mathrm {~cm}$
B) $\quad 20 \mathrm {~cm}$ by $20 \mathrm {~cm}$
C) $\quad 6 \mathrm {~cm}$ by $6 \mathrm {~cm}$
D) $\quad 6 \mathrm {~cm}$ by $4 \mathrm {~cm}$
E) $\quad 7 \mathrm {~cm}$ by $4 \mathrm {~cm}$

Question

The area of a rectangle is 24 square centimeters, and its perimeter is 20 centimeters.Find the dimensions of the rectangle. 
A) $\quad 6 \mathrm {~cm}$ by $7 \mathrm {~cm}$
B) $\quad 20 \mathrm {~cm}$ by $20 \mathrm {~cm}$
C) $\quad 6 \mathrm {~cm}$ by $6 \mathrm {~cm}$
D) $\quad 6 \mathrm {~cm}$ by $4 \mathrm {~cm}$
E) $\quad 7 \mathrm {~cm}$ by $4 \mathrm {~cm}$

Quizplus · Accepted Answer

Let's call the length of the rectangle l and its width w. We know that lw = 24 and 2l + 2w = 20. Simplifying the second equation, we get l + w = 10. Rearranging this equation, we get l = 10 - w. Substituting this expression for l into the first equation, we get (10 - w)w = 24. Simplifying and rearranging, we get w^2 - 10w + 24 = 0. Factoring, we get (w - 4)(w - 6) = 0, so w = 4 or w = 6. Since we want positive dimensions, we choose w = 4. Substituting this value into l + w = 10, we get l = 6. Therefore, the dimensions of the rectangle are 6 cm by 4 cm.

The Area of a Rectangle Is 24 Square Centimeters, and Its