Question

In triangle PQR, PR = 8cm, QR = 4 cm and PL = 5cm. Find (i) the area of triangle PQR (ii) QM​

Answer 1

area of triangle,1/2×base × height
so,
area=1/2×4×5
=10 cm^2

Answer 2

Area of Δ PQR = 10 cm² & QM = 2.5 cm

Step-by-step explanation:

PR = 8 cm

QR = 4 cm

PL = 5 cm

LR² = PR² - PL²

=> LR² = 8² - 5²

=> LR = √39 = 6.245 cm

Area of Δ PLR = (1/2) & PL * LR = (1/2) * 5 *√39 = 15.6 cm²

QR = 4 cm

LQ = LR - QR = 6.245 - 4 = 2.245 cm

Area of Δ PLQ = (1/2) & PL * LQ = (1/2) * 5 * 2.245 = 5.6 cm²

Area of Δ PQR = Area of Δ PLR  - Area of Δ PLQ  = 15.6- 5.6 =10 cm²

Area of Δ PQR = 10 cm²

Area of Δ PQR =  (1/2)* PR * QM  = (1/2) * 8 * QM = 10

=> QM = 2.5 cm

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