Question

for each pair of similar figures use the given areas to find the scale factor from the unshaded figure, then find x.

Answer 1

Answer:

• Scale factor, k=3

,

• x=7m

Explanation:

Let the scale factor be = k

When a figure is enlarged by a scale factor, the area of the scaled image is equal to:

Area of the Original Image x Square of the Scale factor.

Therefore:

$\begin{gathered} \text{Area of shaded figure}=Area\text{ of unshaded figure}\times k^2 \\ 4590=510\times k^2 \\ k^2=\frac{4590}{510} \\ k^2=9 \\ k=3 \end{gathered}$

The scale factor = 3.

Since the scale factor = 3

$x=\frac{21}{3}=7m$