Question

In the figure, FQ is parallel to RS". The length of PT is 3 cm; the length of PQ

is 5 cm; the length of RS is 15 cm. What is the length of RT?
A. 12 cm
B.9 cm
C. 8 cm
D. 10 cm

Answer 1

The measure of length RT is 9 cm .

Explanation:

Given figure as :

The Triangle TRS and Triangle TPQ are similar triangles

I.e Δ TRS ≈ Δ TPQ

And The measure of side PT = 3 cm

The measure of side PQ = 5 cm

The measure of side RS = 15 cm

Let The measure of side RT = x cm

So, From the property of similar triangles

`(\textrm measure of side TR)/(\textrm measure of side TP)` =
`(\textrm measure of side RQ)/(\textrm measure of side PQ)`

I.e
`(TR)/(TP)` =
`(RS)/(PQ)`

Or,
`(x)/(3)` =
`(15)/(5)`

Or,
`(x)/(3)` = 3

∴ x = 3 × 3

I.e x = 9 cm

Hence The measure of length RT is 9 cm . Answer