Question

The length of a rectangle is 3 times longer than its width. If the area of the rectangle is 24 square inches, then what is the perimeter of the rectangle?

Answer 1

=16sqrt(2) inches

Explanation:

Let w = width

The length is 3 times longer than the width

L =3w

A = l*w

24 = (3w) *w

24 = 3w^2

Divide each side by 3

24/3 = 3w^2/3

8 = w^2

Take the square root of each side

sqrt(8) = sqrt(w^2)

sqrt(4)sqrt(2) = w

2sqrt(2) =w

Now we can find the length

L = 3w

L = 3(2sqrt(2))

L =6sqrt(2)

The final step is to find the perimeter

Perimeter is 2(l+w)

P =2(l+w)

=2(2sqrt(2) +6sqrt(2))

Combine like terms

=2(8sqrt(2))

=16sqrt(2)

Answer 2

Answer: The answer is 16√2 cm.

Step-by-step explanation: Given that there is a rectangle with length 3 times than its width. We are to find the perimeter of the rectangle.

Let 'w' represents the width of the rectangle.

Then, its length will be 3w.

Also, area of the rectangle = 24 square inches.

Therefore,

`3w* w=24\\\\\Rightarrow 3w^2=24\\\\\Rightarrow w^2=8\\\\\Rightarrow w=2\sqrt 2.`

So, width = 2√2 inches and length = 6√2 inches.

Thus, perimeter of the rectangle = 4√2 + 12√2 = 16√2 cm.