Question

ABCand XYZ are similar triangles. The lengths of the two sides are shown. Find the lengths of the third side of each triangle

Answer 1

Given:

AC = 9.6

AB = 4

BC = a

XZ = y

XY = 2.5

YZ = 7.5

To find the lengths of the third side of each triangle apply the ratio for similar triangles.

Since both triangles are similar, the corresponding sides are proportional.

$\frac{AC}{XZ}=\frac{AB}{XY}=\frac{BC}{YZ}$

• For BC:

We have:

$\frac{AB}{XY}=\frac{BC}{YZ}$

Input values into the equation:

$\begin{gathered} \frac{4}{2.5}=\frac{a}{7.5} \\ \\ \text{Cross multiply:} \\ 2.5(a)=7.5(4) \\ \\ 2.5a=30 \\ \\ \text{Divide both sides by 2.5:} \\ \frac{2.5a}{2.5}=\frac{30}{2.5} \\ \\ a=12 \end{gathered}$

Therefore, the length of BC is 12.

• For XZ:

We have the equation:

$\frac{AC}{XZ}=\frac{AB}{XY}$

Input values into the equation:

$\begin{gathered} \frac{9.6}{y}=\frac{4}{2.5} \\ \\ \text{Cross multiply:} \\ 4y=9.6(2.5) \\ \\ 4y=24 \\ \\ \text{Divide both sides by 4:} \\ \frac{4y}{4}=\frac{24}{4} \\ \\ y=6 \end{gathered}$

Therefore, the length of XZ is 6

ANSWER:

• a = 12

• y = 6