Question

In the figure line PQ|| side BC,AP=2.4cm,PB=7.2cm,QC=5.4cm then find AQ

Answer 1

Complete question:

In ΔABC, line PQ|| side BC,AP=2.4cm,PB=7.2cm,QC=5.4cm then find AQ.

Answer:

The length of AQ = 1.8cm

Step-by-step explanation:

Given,

The line PQ is parallel to the side BC of the triangle.

AP = 2.4cm

PB = 7.2cm

QC = 5.4cm

To find,

The length of AQ

Recall the theorem,

Basic Proportionality Theorem

If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio

Since the line, PQ is parallel to the side BC of the triangle,

then by the Basic proportionality theorem, we have

$\frac{AP}{PB} = \frac{AQ}{QC}$

By substituting the given values we get

$\frac{2.4}{7.2} = \frac{AQ}{5.4}$

Cross multiplying, we get

7.2 × AQ = 2.4×5.4

AQ = $\frac{2.4X5.4}{7.2}$

=1.8

The length of AQ = 1.8cm

#SPJ3

Answer 2

Answer:

The length of the AQ is 1.8 cm

Step-by-step explanation:

Given : The side AP=2.4cm, PB=7.2cm,QC=5.4cm

To find: The length of AQ in the triangle

Solution:

In the given triangle

The side PQ is perpendicular to BC

PQ || BC

∠APQ = ∠ABC

According to the corresponding angles

∠AQP=∠ACB

According to the AA criteria

△APQ∼△ABC

$\frac{AP}{AB} = \frac{AQ}{AC}$

⇒ $\frac{AB}{AP} = \frac{AC}{AQ}$

⇒ $\frac{AB}{AP} - 1 = \frac{AC}{AQ} -1$

⇒ $\frac{PB}{AP} = \frac{QC}{AQ}$

⇒ $\frac{7.2}{2.4} = \frac{5.4}{AQ}$

⇒ AQ = 1.8 CM

Final answer:

The length of the side AQ is 1.8 cm

#SPJ3