Find the altitude (in cm) from the vertex Q to side PR of ΔPQR with side lengths PQ = 40 cm, PR = 40 cm and QR = 60 cm.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. .
In ΔPQR, PQ = 40 cm, PR = 40 cm, and QR = 60 cm
Semi-Perimeter (s) = (40 + 60 + 40)/2 = 140/2 = 70 cm
Area of ΔPQR = √[s(s - PQ)(s - QR)(s - PR)]
= √[70(70 - 40)(70 - 60)(70 - 40)]
= √[70 × 30 × 10 × 30]
= √[630000]
= 300√7 cm2
Let the altitude from Q to PR be QS.
Area = (1/2) × Base × Height
⇒ 300√7 = (1/2) × 40 × QS
⇒ 300√7 = 20QS
⇒ QS = (300√7)/20 = 15√7 cm
Therefore, the altitude from vertex Q to side PR is 15√7 cm.