Question

A rectangle has an area of 384 m². The length and the width of the rectangle are changed by a scale factor of 0.75.

What is the area of the new rectangle?

Answer 1

We are tasked to solve for the area of the new rectangle. The formula of solving area of the rectangle is A = width * length

Old triangle Area = 384 m² = w * l
New triangle Area we have:
Area = w * 0.75l
384 m² = w*0.75l
384 / 0.75 = w*l
288 m² = w*l

The answer is 288 m².

Answer 2

Answer:
`216\ m^2`

Explanation:

A rectangle has an area of 384 m².

Let l and w are the length and the width of the original rectangle, such that the area of the rectangle is given by ;-

`A=lw=384`

The length and the width of the rectangle are changed by a scale factor of 0.75 will be:

`l'=0.75l\\\\w'=0.75w`

Now, the area of the new rectangle will be :

`A=l'w'=0.75l*0.75w\\\\=(0.75)^2(lw)\\\\=(0.5625)(384)=216\ m^2`

Hence, the area of the new rectangle
`=216\ m^2`