Question

Two sides of a triangle are $10cm$ and $15cm$and the base is $20cm$ long. If another triangle similar to the first triangle has the base measuring $32cm,$find the other two sides of the triangle

Answer 1

Step 1: Note the given data and figure

Let $ABC$ and $PQR$ be two triangles such that, $△ABC~△PRQ$.

Let $AB=10cm,AC=15cm,BC=20cm$and $QR=32cm$

The diagrams of $△ABC$ and $△PQR$ are shown below

Step 2: Applying the property of similar triangles.

Similar triangle property: If two triangles are similar, then the ratios of the corresponding sides are equal.

Since $△ABC~△PRQ$, so

$$\begin{gathered} \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR} \\ \Rightarrow \frac{10}{PQ}=\frac{15}{PR}=\frac{20}{32} \end{gathered}$$

Taking the first and the last ratios

$$\begin{gathered} \frac{10}{PQ}=\frac{20}{32} \\ \Rightarrow PQ=\frac{32\times 10}{20} \\ \Rightarrow PQ=16cm \end{gathered}$$

Taking the second and the last ratios

$\begin{array}{rcl}\frac{15}{PR}& =& \frac{20}{32}\\ & \Rightarrow & PR=\frac{32\times 15}{20}\\ & \Rightarrow & PR=24cm\end{array}$

Hence, the measurements of the other two sides of the second triangle are $16cm$ and $24cm$.