Question

the area of a rectangle is (x^2 + 8x + 12) cm^2. If the length of the rectangle is (x+6) cm, show that its breadth is (x+2) cm.

Answer 1

Step-by-step explanation:

area=x²+8x+12

length=x+6

breadth =x+2

area=l×b

if we multiply l and b and if we get the area as x²+8x+12then breadth is correct one

(x+6)(x+2)

x(x+6)+2(x+6)

x²+6x+2x+12

x²+8x+12

the value of the breadth is correct

Answer 2

★ Given :

Area of triangle = x² + 8x + 12 cm²

length = (x+6)cm

★ To show :

breadth = (x+2) cm

★ Solution :

We know that,

Area of a rectangle = length × breadth

by putting values

(x² + 8x + 12) = (x+6) × breadth

by diving (x² + 8x + 12) into factors

using middle term splitting

x² + 6x + 2x + 12

x(x+6) + 2(x+6)

= (x+2)(x+6)

(x+2)(x+6) = (x+6) × breadth

$breadth = \dfrac{(x+2)\cancel{(x+6)}}{\cancel{(x+6)}}$

$\purple{\therefore \: breadth = (x+2)}$

Hence, verified..