Question

1. If A ABC ~ APQR, find the missing quantities in the following table which are marked
by question sign (?):
8x²
Sr. No.
AB
BC
CA
PQ
QR
RP
(1)
4 cm
(?)
9 cm
2.4 cm
3.6 cm
(?)
Tea
(2)
5 cm
5 cm
(?)
7 cm
(?)
11.2 cm​

Answer 1

Step-by-step explanation:

The sides of △PQR will be

2

3

times the sides of △ABC

∴PQ=

2

3

×AB=

2

3

×3.6=5.4 cm

QR=

2

3

×BC=

2

3

×4=6 cm

PR=

2

3

×AC=

2

3

×4.2=6.3 cm

Construction:

Step 1: Draw base PR=6.3 cm with a ruler.

Step 2: Place the compass on point P and measure an arc with length of the compass as PQ=5.4 cm.

Step 3: Place the compass on point R and measure an arc with length of the compass as QR=6 cm.

Step 4: Mark the intersection point of the arcs in steps 2 and 3 as point Q and draw lines joining P−Q and R−Q.

△PQR is the required triangle.

Measure the ∠PRQ using a protractor, which comes out to be 52

∘