Question

In triangle PQR, PQ=14cm , PR=10 cm , angle P= 60°. a) find the length of the perpendicular from R to PQ. b) find the area of triangle PQR​

Answer 1

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Answer 2

Given:

In triangle PQR,

PQ = 14cm, PR = 10cm and ∠P = 60°

To Find:

a). The length of the perpendicular from R to PQ.

b). The area of triangle PQR.

Solution:

a). By Pythagoras Theorem,

H² = P² + B²

this can be written as,

PR² = OR² + OP²

Where, PR = H = 10cm.

OP = (PQ/2) = B = 14/2 cm = 7cm.

so, OR² = PR² - OP²

OR² = 100 - 49 cm²

OR² = 54cm²

OR =√54 cm = 3√6cm.

b). Area of Triangle = 1/2 × base × height.

For Triangle PQR,

Base = PQ = 14cm.

Height = OR = 3√6cm.

so, Area of Triangle PQR = 1/2 × 14cm × 3√6cm.

Area of Triangle PQR = 21√6cm²

Hence, a). The length of the perpendicular from R to PQ is 3√6cm.

b). The area of triangle PQR is 21√6cm².