Question

Construct APQR, whose perimeter is 8.4 cm and PQ : QR : PR = 5: 7:9.​

Answer 1

Answer:

20,28,36cm

Step-by-step explanation:

let the sides be x

perimeter =5x×7x×9x

84=21x

4=x

so, 5×4 = 20 cm

7×4 = 28 cm

9×4 = 36cm

Answer 2

Step-by-step explanation:

Given :-

In ∆PQR, PQ : QR : PR = 5: 7:9.and Perimeter is 8.4 cm

To find :-

Construct ∆PQR ?

Solution :-

Given that

The ratio of the sides in ∆PQR = 5:7:9

PQ : QR : PR = 5:7:9

Let PQ = 5X cm

Let QR = 7X cm

Let PR = 9X cm

Perimeter of the triangle is the sum of all sides

=> P(∆PQR) = PQ+QR+PR

=> P(∆PQR) = 5X+7X+9X = 21X cm

According to the given problem

Perimeter of the triangle = 8.4 cm

=> 21X = 8.4

=> X = 8.4/21

=> X = 0.4 cm

If X = 0.4 cm then PQ = 5X = 5(0.4) = 2 cm

If X = 0.4 cm then QR = 7X = 7(0.4) = 2.8 cm

If X = 0.4 cm then PR = 9X = 9(0.4) = 3.6 cm

Therefore, PQ = 2 cm

QR = 2.8 cm

PR = 3.6 cm

Construction :-

See the attachment for the rough diagram and the construction.

Steps of Construction:-

→ Draw a line segment QR with 2.8 cm

→ Draw an arc with 2 cm from Q and draw another arc with 3.6 cm from R.

→ Name the intersecting point as P.

→ Join P and Q , Join R and P.

→ ∆PQR is the required triangle.