Question

PQRS is a parallelogram and RT perpendicular Ps. If ar(∆PQR)=7.2 sq.cm and RT=3.2 cm, find the length of PS.​

Answer 1

Answer

4.5 cm

$\rule{200}2$

Given

★ RT perpendicular to PS.

★ ar(∆PQR) = 7.2 cm²

★ RT = 3.2 cm

To Find

The length of PS.

Solution

We know that diagonals of a //gm divides it into two congruent triangles.

Congruent triangles have equal area.

→ ar(∆PQR) = ar(∆PRS)

Now, given ar (∆PQR) = 7.2 cm²

→ ar(∆PRS) = 7.2 cm²

But, ar(∆PRS) = 1/2 × PS × RT

→ 1/2 × PS × RT = 7.2

→ 1/2 × PS × 3.2 = 7.2

→ PS × 1.6 = 7.2

→ PS = 7.2/1.6

→ PS = 4.5 cm

Answer 2

$\huge \red { \boxed{ \boxed{ \mathsf{ \mid \ulcorner Answer : \urcorner \mid }}}}$

A.T.Q,

$\large{\sf{ar(\triangle PQR) \: = \: ar(\triangle PRS)}}$

Area of Δ PQR = 7.2 cm²

So, area of ΔPRS = 7.2 cm²

______________________________

In ΔPRS

$\large{\sf{Area \: = \: \frac{1}{2} \times B \times H}}$

Now put values

$\large{\sf{7.2 \: = \: \frac{1}{2} \times PS \times PR}}$

$\large{\sf{7.2 \: = \: \frac{1}{2} \times PS \times 3.2}}$

$\large{\sf{PS \: = \: \frac{7.2}{1.6}}}$

$\huge{\sf{PS \: = \: 4.5 \: cm}}$