Question

The area of a rectangle is 36 square centimeters; its perimeter is 30 centimeters. What are the dimensions of the rectangle?

Answer 1

Answer:

12cm x 3cm

Step-by-step explanation:

(12 + 3) x 2 = perimeter = 30 cm, 12 x 3 = area = 36

Answer 2

Answer:

The dimensions of the rectangle are 12 cm × 3 cm.

Step-by-step explanation:

Let the length of the rectangle be l and the width of the rectangle is w.

The area of a rectangle is 36 square centimeters.

$A=l\times w$

$36=l\times w$                .... (1)

The perimeter of rectangle is 30 centimeters.

$P=2(l+w)$

$30=2(l+w)$

$15=l+w$

$l=15-w$                   .... (2)

Using (1) and (2), we get

$36=(15-w)\times w$

$36=15w-w^2$

$w^2-15w+36=0$

$w^2-12w-3w+36=0$

$w(w-12)-3(w-12)=0$

$(w-12)(w-3)=0$

$w=12,3$

The width of the rectangle is either 12 or 3.

If the width of the rectangle is 12, then

$l=`15-12=3$

If the width of the rectangle is 3, then

$l=`15-3=12$

Therefore the dimensions of the rectangle are 12 cm × 3 cm.