Question

the breadth of a rectangle is 3 cm less than its length. If the area of the rectangle is 88 cm^2. Find its perimeter.

Answer 1

GIVEN:-

${\underline{\rm{\blue{Let}}}}$

• $\rm{Length\:of\:Rectangle=x}$

• $\rm{Breadth\:of\: Rectangle=(x-3)}$

• $\rm{Area\:of\:Rectangle=88cm^2}$

TO FIND:-

• The Perimeter of Rectangle

FORMULAE USED:-

• ${\boxed{\rm{Area\:of\:Rectangle=L×B}}}$

Where,

L = Length

B= Breadth.

• ${\boxed{\rm{Perimeter\:Of\: Rectangle=2(L+B)}}}$

Where,

L = Length

B= Breadth.

$\implies\rm{Area\:of\:Rectangle=L×B}$

$\implies\rm{88cm^2=(x)(x-3)}$

$\implies\rm{88cm^2=x^2-3x}$

$\implies\rm{x^2-3x-88=0}$

$\implies\rm{x^2-11x+8x-88=0}$

$\implies\rm{x(x-11)+8(x-11)=0}$

$\implies\rm{(x+8)(x-11)=0}$

$\implies\rm{x+8=0}$

$\implies\rm{x=-8}$

$\implies\rm{x-11=0}$

$\implies\rm{x=11}$

Hence, The length can' be negative so x=11.

Now,

$\implies\rm{Length=x=11cm}$

$\implies\rm{Breadth=x-3=8cm}$

Now,

$\implies\rm{Perimeter=2(L+B)}$

$\implies\rm{Perimeter=2(11+8)}$

$\implies\rm{Perimeter=38cm}$

Hence, The perimeter of the Rectangle is 38cm.

Answer 2

Given :–

• The breadth of a rectangle is 3 cm less than its length .
• Area of the rectangle is 88 cm² .

To Find : –

• Perimeter of the rectangle .

Solution : –

Let, the length of the rectangle be x .

then the breadth of the rectangle will be ( x - 3 ) .

We have : –

• Length = x
• Breadth = ( x - 3 )
• Area = 88 cm²

We know that –

Area of rectangle = length × breadth

→ 88 = (x) × (x - 3)

→ 88 = x² - 3x

→ x² - 3x - 88 = 0

→ x² - (11 - 8)x - 88 = 0

→ x² - 11x + 8x - 88 = 0

→ x(x - 11) + 8(x - 11) = 0

→ (x - 11) (x + 8) = 0

x - 11 = 0

→ x = 11

x + 8 = 0

→ x = - 8

As we know the length of a rectangle can't be negative so , the length is 11 cm .

Breadth of the rectangle : –

x - 3

→ 11 - 3

→ 8 cm .

Perimeter of the rectangle : –

P = 2( l + b )

→ P = 2( 11 + 8 )

→ P = 2 × 19

→ P = 38 cm .

Hence, the perimeter of the rectangle is 38 cm .