Question

ΔABC ~ ΔPQR. In ΔABC, AB = 3.6 cm, BC = 4 cm, AC = 4.2 cm. The corresponding sides of ΔABC and ΔPQR are in the ratio 2 : 3. Construct ΔABC and ΔPQR.

Answer 1

Given: AB = 3.6 cm, BC = 4 cm, AC = 4.2 cm

As ΔABC ~ ΔPQR

∴ Their corresponding sides are proportional.

`(AB)/(PQ) = (BC)/(QR) = (AC)/(PR) = 2/3`

`3.6/(PQ) = 4/(QR) = 4.2/(PR) = 2/3`  ...(i)

Now, `3.6/(PQ) = 2/3`

PQ = `(3.6 xx 3)/2`

PQ = 1.8 × 3

PQ = 5.4 cm

Now, `4/(QR) = 2/3`  ...[From (i)]

QR = `(4 xx 3)/2`

QR = 2 × 3

QR = 6 cm

Now, `4.2/(PR) = 2/3`  ...[From (i)]

PR = `(4.2 xx 3)/2`

PR = 2.1 × 3

PR = 6.3 cm

Construct Triangle ΔABC

1. Draw BC = 4 cm using a ruler.
2. Using a compass, set AB = 3.6 cm, place the compass pointer on B, and draw an arc.
3. Similarly, set AC = 4.2 cm, place the compass pointer on C, and draw another arc intersecting the first arc. Mark this intersection as A.
4. Join A to B and A to C to complete ΔABC.

Construct Triangle ΔPQR Similar to ΔABC

1. Draw QR = 6 cm (since BC corresponds to QR).
2. Using a compass, set PQ = 5.4 cm, place the compass pointer on Q, and draw an arc.
3. Similarly, set PR = 6.3 cm, place the compass pointer on R, and draw another arc intersecting the first arc. Mark this intersection as P.
4. Join P to Q and P to R to complete ΔPQR.