Question 85·Easy·Geometry and Trigonometry

First, multiply the length of rectangle $P$ by $1.5$ to get the length of rectangle $Q$. Then do the same with the width of rectangle $P$ to get the width of rectangle $Q$.

Once you know the new length and width of rectangle $Q$, use the area formula for a rectangle, $\text{area} = \text{length} \times \text{width}$, and then match your result to one of the answer choices.

In Desmos, type the expression 6*4*(1.5)^2. The value that Desmos outputs is the area of rectangle $Q$; compare that number to the answer choices given in the problem.

Rectangle $P$ has length $6\text{ cm}$ and width $4\text{ cm}$. Rectangle $Q$ is similar to rectangle $P$, and the length of $Q$ is $1.5$ times the length of $P$.

That means the scale factor from rectangle $P$ to rectangle $Q$ (for all side lengths) is $1.5$.

The length of rectangle $P$ is $6\text{ cm}$. The length of rectangle $Q$ is $1.5$ times this length:

So the length of rectangle $Q$ is $9\text{ cm}$.

Because the rectangles are similar, every side of rectangle $Q$ is multiplied by the same scale factor $1.5$.

The width of rectangle $P$ is $4\text{ cm}$, so the width of rectangle $Q$ is:

So the width of rectangle $Q$ is $6\text{ cm}$.

The area of a rectangle is $\text{length} \times \text{width}$.

For rectangle $Q$:

• Length $= 9\text{ cm}$
• Width $= 6\text{ cm}$

So the area is

The area of rectangle $Q$ is $54$ square centimeters, which corresponds to answer choice C) 54.