Question

A rectangular building lot is three times as long as it is wide. Find a function that models its area A in terms of its width W

Answer 1

3w * w = A;   This would be the correct function

Answer 2

The function that models the rectangular building area A in terms of its width W is $A = 3w^{2}$

From the question, a rectangular building lot is three times as long as it is wide.

Let the width be $w$ and the length be $l$

Then we can write from the above statement that

$l = 3w$ ------ (1)

Now, for a function that models its area A in terms of its width w, that means we should write an equation for the area in terms of its width only.

From the formula for area of a rectangle,

Area = length × width

∴ $A = l \times w$

From equation (1), we have that $l = 3w$

Substitute this into the area formula,

$A = l \times w$

We get

$A = 3w \times w$

Then,

$A = 3w^{2}$

Hence, the function that models the rectangular building area A in terms of its width W is $A = 3w^{2}$

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