Question

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the pentagons abcde and pqrst are similar. find the length x of qr.

Explanation:

Step1: Find the scale - factor

Compare corresponding sides. Let's use sides $AB$ and $PT$. The length of $AB = 4$ and $PT=7.2$. The scale - factor $k=\frac{PT}{AB}=\frac{7.2}{4}=1.8$.

Step2: Calculate $x$

Side $BC = 5$ corresponds to side $QR$. Since the pentagons are similar, $x = BC\times k$. Substitute $BC = 5$ and $k = 1.8$ into the formula, so $x=5\times1.8 = 9$.

Answer:

$9$