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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

Verified Answer :

Answer:

Option C is correct

\(l = x+4\) unit and \(w = x+3\) unit

Step-by-step 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

Answer: C

Step-by-step explanation:

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