Question

rectangles abcd and efgh are similar. the length of each side of efgh is 6 times the length of the corresponding side of abcd. the area of abcd is 90 square units. what is the area, in square units, of efgh? a 15 b 36 c 540 d 3,240

Explanation:

Step1: Recall the ratio - of - areas formula for similar rectangles

If two similar figures have a scale factor of \(k\), the ratio of their areas is \(k^{2}\). Here, the scale factor \(k = 6\) since the length of each side of \(EFGH\) is 6 times the length of the corresponding side of \(ABCD\).

Step2: Calculate the area of \(EFGH\)

Let \(A_1\) be the area of \(ABCD\) and \(A_2\) be the area of \(EFGH\). The formula is \(\frac{A_2}{A_1}=k^{2}\). Given \(A_1 = 90\) square units and \(k = 6\), then \(A_2=A_1\times k^{2}\). Substitute \(A_1 = 90\) and \(k = 6\) into the formula: \(A_2=90\times6^{2}\).
\[

$$\begin{align*} A_2&=90\times36\\ & = 3240 \end{align*}$$

\]

Answer:

D. 3,240