Question

The area of a rectangle, measured in cm? is numerically equal to its perimeter, measured in cm.

The length of the rectangle is 4 times its width.
Calculate the width and length of the rectangle.
Give your answers in centimetres.

Answer 1

Length : 10cm

Width : 2.5cm

Let the length be l & width be w.

ATQ,

• l = 4w.....(1)

Also,

• 2(l +w) = lw........(2)

substituting the value of l from equation (1) into equation (2),

we get,

• 2(4w + w) = 4w*w
• 10w = 4w²
• 10 = 4w
• w = 10/4
• w = 2.5cm

hence, the width of the rectangle would be equal to 2.5 cm

and the length being 4 times the width would be equal to :

• l = 2.5cm x 4
• l = 10cm

Therefore,the length would be equal to 10 cm.

Answer 2

width = 2.5 cm , length = 10 cm

Explanation:

let width be w then length = 4w ( 4 times the width )

the area (A) of a rectangle is calculated as

A = length × width = 4w × w = 4w²

the perimeter (P) is calculated as

P = 2( length + width) = 2(4w + w) = 2(5w) = 10w

given that area and perimeter are numerically equal , then

4w² = 10w ( subtract 10w from both sides )

4w² - 10w = 10w - 10w , that is

4w² - 10w = 0 ← factor out 2w from each term on the left side

2w(2w - 5) = 0 ← in factored form

2w = 0 ⇒ w = 0

2w - 5 = 0 ( add 5 to both sides )

2w = 5 ( divide both sides by 2 )

w =
`(5)/(2)` = 2.5

but w > 0 , then w = 2.5

that is

width = 2.5 cm

length = 4w = 4 × 2.5 = 10 cm