Question

The given pair of triangles are similar. Find X and Y.

Answer 1

Given that the pair of triangles are similar, then their corresponding sides are in proportion, this means that:

`\frac{\text{longer leg of the triangle on the left}}{\text{shorter leg of the triangle on the left}}=\frac{\text{longer leg of the triangle on the right}}{\text{shorter leg of the triangle on the right}}`

Substituting with the information of the diagram:

`(27)/(x)=(x)/(9)`

Cross multiplying:

`\begin{gathered} 27\cdot9=x\cdot x \\ 243=x^2 \\ \sqrt[]{243}=x \\ 15.58\approx x \end{gathered}`

Considering the triangle on the left, and applying the Pythagorean theorem with c = y (the hypotenuse), a = 27, and b = x (the legs), we get:

`\begin{gathered} c^2=a^2+b^2 \\ y^2=27^2+x^2 \\ y^2=729+243 \\ y^2=972 \\ y=\sqrt[]{972} \\ y\approx31.18 \end{gathered}`