Question

find QR in the figure

Answer 1

Required Answer:-

Here ∆PQS is divided into two smaller triangles ∆PQR and ∆PRS. We just need to prove them congruent, such that we can determine the length of QR.

Here,

In ∆PQR and ∆PRS,

• PQ = PS = 20 cm (given)
• < QPR = < SPR (also, given)
• PR = common.

$\therefore$ ∆PQR ≅ ∆PRS (By SAS congurence)

Then, QR = RS (CPCT)

So the length of QR will be 8 cm too$.$

Answer 2

QR = 8cm

Step-by-step explanation:

Given:

• PS = 20cm

• RS = 8cm

To find:

• QR

Solution:

• In the given triangle, ∆QPR and ∆RPS

• Angle QPR = Angle SPR [Given]

• Angle QRP = Angle SRP [Common]

By AA similarity,

• ∆QPR is similar to ∆RPS

•We know that in a similar triangle, the corresponding sides are equal.

Therefore:

• QR/RS = PR/PR

• QR/RS = 1

• QR = RS

Hence, QR = RS = 8cm