Question

The area of a rectangle is found by multiplying the length by the width: A = lw. A certain rectangle has an area of x2 + 7x + 12.

Factor the trinomial to find the length and width of the rectangle.
l = x + 6; w = x + 2
l = x + 5; w = x + 7
l = x + 4; w = x + 3

Answer 1

Answer: C

Explanation:

Answer 2

Option C is correct

`l = x+4` unit and
`w = x+3` unit

Explanation:

Area of a rectangle is given by:

`A =lw` ....[1]

where

A is the area of rectangle

l is the length of a rectangle

w is the width of a rectangle.

As per the statement:

A certain rectangle has an area of
`x^2 + 7x + 12`

⇒
`A = x^2+7x+12`

Now factor this trinomial :

`A = x^2+4x+3x+12`

⇒
`A = x(x+4)+3(x+4)`

⇒
`A=(x+4)(x+3)` unit square

On comparing with [1] we have;

`l = x+4` unit and
`w = x+3` unit

Therefore,the length and width of the rectangle are:

`l = x+4` unit and
`w = x+3` unit