Question

In ∆ DEF, line PQ || side EF, If DP = 2.4, PE = 7.2, PQ = 1 then find QF.

Answer 1

Given that,

In Δ DEF, line PQ ║EF

DP = 2.4

PE = 7.2

PQ = 1

Suppose, DQ = 1

PQ is parallel to EF it means, it divided the side DF and DE in proportional ratio.

We need to calculate the value of DE

Using total length of DE

$DE=DP+PE$

Put the value into the formula

$DE=2.4+7.2$

$DE=9.6$

Let L be the total length of side DF.

We need to calculate the value of L

Using ratio of side

$\dfrac{DP}{DE}=\dfrac{DQ}{DF}$

Put the value into the formula

$\dfrac{2.4}{9.6}=\dfrac{1}{L}$

$L=\dfrac{9.6}{2.4}$

$L=4$

We need to calculate the length of QF

Using length of DF

$DF=DQ+QF$

$QF=DF-DQ$

Put the value into the formula

$QF=4-1$

$QF=3$

Hence, The length of QF is 3.