Question

A rectangle length is 6cm more than its breadth the area is 112cm2.what is its perimeter?

Answer 1

Let the breadth of the rectangle be "x" cm

The length will become :-

(x+6) centimeters

$\rule{200}{2}$

Area of the rectangle (given ) = 112 sq.centimeters

$\rule{200}{2}$

we know that :-

The area of the rectangle = length * breadth

thus,

Applying the formula :-

$(x+6)x=112\\ \\ \\\implies x^{2}+6x = 112\\ \\ \\\implies x^{2}+6x-112=0\\ \\ \\\implies x^{2}+14x-8x-112=0\\ \\\implies x(x+14)-8(x+14)=0\\ \\ \\\implies (x+14)(x-8)=0\\ \\ \\\implies x+14=0\\ \\x=(-14)\\ \\ \\\implies x-8=0\\ \\x=8$

$\rule{200}{2}$

since the side of a figure can never be a negative number;

hence,

x cannot be equal to (-14)

$\rule{200}{2}$

This Implies :-

X = 8 centimeter

$\rule{200}{2}$

Breadth = x = 8 Cm

Length = x+6 = 14 Cm

$\rule{200}{2}$

Perimeter = 2(L+B)

= 2(14+8)

=2(22)

=44 Centimeters