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.

`(AC)/(XZ)=(AB)/(XY)=(BC)/(YZ)`

• For BC:

We have:

`(AB)/(XY)=(BC)/(YZ)`

Input values into the equation:

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

Therefore, the length of BC is 12.

• For XZ:

We have the equation:

`(AC)/(XZ)=(AB)/(XY)`

Input values into the equation:

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

Therefore, the length of XZ is 6

ANSWER:

• a = 12

• y = 6