Question

The longth of rectangular is 3 cm more than its
breadth. If the area of the rectangle Ps 88m²
find its perimeter​

Answer 1

To Find:-

• Find the perimeter of rectangle.

Given:-

• The longest side of rectangle is 3 cm more than its shortest side.
• The area of rectangle is 88 cm²

Solution:-

Let the breadth be " x "

Then the length is " x + 3 "

As we know that:-

$\tt\implies \: Area = l \times b$

$\tt\implies \: 88 = ( x + 3 ) \times x$

$\tt\implies \: 88 = { x }^{ 2 } + 3x$

$\tt\implies \: { x }^{ 2 } + 3x - 88 = 0$

$\tt\implies \: { x }^{ 2 } - 8x + 11x - 88$

$\tt\implies \: x( x - 8 ) + 11( x - 8 ) = 0$

$\tt\implies \: ( x + 11 ) ( x - 8 ) = 0$

$\tt\implies \: x = - 11 \: or \: 8$

Let us take x = 8:-

Hence,

• $\tt \: Breadth = 8 \: cm$

• $\tt \: Length = x + 3 = 11 \: cm$

Therefore:-

$\tt\implies \: Perimeter = 2( l + b )$

$\tt\implies \: Perimeter = 2( 11 + 8 )$

$\tt\implies \: Perimeter = 2( 19 )$

$\tt\implies \: Perimeter = 38 \: { cm }^{ 2 }$