Question

A rectangle has a perimeter of 20 inches and an area of 24 square inches. What are the length and width of the rectangle?

Answer 1

Length = 6in

Width = 4in

Explanation:

The formula for solving the perimeter of a rectangle is:

P = 2(L+W)

The formula for finding the area of a rectangle is:

A = L x W

If we substitute our values, we will get:

P = 2(6 + 4)

P = 2(10)

P = 20in

A = 6 x 4

A = 24in²

Answer 2

When l = 6 ⇒ w = 4

when l = 4 ⇒w = 6

Explanation:

We have given perimeter and area of rectangle.

Perimeter = P = 20 inches and Area = A = 24 square inches

We have to find the length and width of the rectangle.

Let l is length and w is width of rectangle.

The formula of Perimeter is :

P = 2(l+w)

The formula of area is :

A = l × w

Given values :

P = 2(l+w) = 20

l+w = 10

w = 10-l eq(1)

A = l × w = 24 eq(2)

Putting eq(1) in eq(2), we have

A = l × (10-l) = 24

10l-l² = 24

l²-10l +24= 0

Applying factorization to above equation, we have

(l-6)(l-4) = 0

Applying Zero-Product rule , we have

l-6 = 0 or l-4 = 0

l = 6 or l = 4

Putting above values in eq(1) , we have

When l = 6 ⇒ w = 10-6

w = 4

when l = 4 ⇒w = 10-4

w = 6

Answer is :

When l = 6 ⇒ w = 4

when l = 4 ⇒w = 6