Question

a rectangle has an area of 135 square meters and has a width that is 6 meters shorter than its length what is the perimeter of the rectangle​

Answer 1

The perimeter of the rectangle is 48 m.

Explanation:

Given:

Area of rectangle=153 sq.m

and

width=b and length=l

b=(l-6) m

To find :

Perimeter of given rectangle

Solution:

we know that the

area of rectangle is given by,

`l*b=135`

`l(l-6)=135`

`l^2-6l-135`=0

solve this quadratic equation,

we get ,

`(l+9)(l-15)`

length will not be negative

therefore l=15 m

hence,
`b=l-6`

`b=15-6`

b= 9 m

Now perimeter is

`2(l+b)`

=
`2(15+9)`

=48 m

Answer 2

Explanation:

length = x m

Width = (x - 6) m

Area = 135 sq.m

length * width = 135

x*(x-6) = 135

x*x - x*6 -135 = 0

x²- 6x - 135 = 0

x² - 15x + 9x - 9*15 = 0

x(x - 15) + 9(x-15) = 0

(x-15)(x + 9) = 0

x - 15 = 0

{x+9=0 is ignored because measurement cannot be a negative number}

x= 15

length = 15 m

width = x - 6 = 15 - 6 = 9 m

Perimeter = 2*(length + width)

= 2*(15 + 9) = 2 * 24 = 48 m