Question

a rectangle is 4 times as long as it is wide. if the area is 36 square feet, find its perimeter.

Answer 1

Answer:

30 feet²

Step-by-step explanation:

Given: Length of rectangle is 4 times as it is wide.

          Area of rectangle is 36 feet²

Lets assume the width of rectangle be "w"

∴ Length of the rectangle will be 4w.

Now, using the formula for Area of rectangle to know width and length of rectangle.

Formula; Area of rectangle= $width\times length$

⇒ $36= w\times 4w$

⇒ $36= 4w^{2}$

Dividing both side by 4

⇒ $\frac{36}{4} = w^{2}$

⇒$9= w^{2}$

Taking square root on both side. remember; √a²=a or -a

⇒$w=\sqrt{9}$

∴ $w=3\ feet\ or -3\ feet, however, \ -3\ is\ ignored\ as\ length\ cannot\ be\ negative$

Next, subtituting the value of width to find legth of rectangle.

Length= $4w$

∴ Length= $4\times 3= 12\ feet$

Lets find the Perimeter of rectangle now.

Formula; Perimeter= $2l+2w$, where l = length and w= width

⇒ $Perimeter = 2\times 12+2\times 3$

⇒ $Perimeter= 24+6$

∴ Perimeter= $30 feet^{2}$

Hence, perimeter of the rectangle is 30 feet²