Solve for the given length. The length of a rectangle is 3m longer than its width. The area of the rectangle is 154^2. What is the width of the rectangle?

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If the length of a rectangle is 3m longer than its width, then:

L=W+3

Is the area really 154^2? Or is it 154m^2? If yes, then:

A=LW

154 = (W+3) (W)

154 = (W^2+3W)

0=W^2+3W-154

0 = (W-11) (W+14)

This means either (W-11) or (W+14) is equal to zero so:

W=11 and W=-14

To find out let's substitute the numbers:

154 = (11+3) (11)

154=154

Therefore, the width of the rectangle is 11m

By definition the area of a rectangle is given by:

A = (w) * (l)

Where,

w: width

l: long

We rewrite the expression based on:

"The length of a rectangle is 3m longer than its width"

A = (w) * (w + 3)

We substitute the value of the area:

154 ^ 2 = (w) * (w + 3)

Rewrite:

23716 = w ^ 2 + 3w

w ^ 2 + 3w-23716 = 0

We solve the polynomial:

w = 152.5

Note: the other root is negative.

Answer:

the width of the rectangle is:

w = 152.5 m