In The diagram, R is a point on the side QS of PQS. Given that PQ= 5cm, QR=3cm,RS=4cm and PS = √74cm, find (a) the lenght of PR, (b) the shortest distance from Q to PS
Answers
Given : R is a point on the side QS of PQS. Given that PQ= 5cm, QR=3cm,RS=4cm and PS = √74cm
To find : (a) the lenght of PR, (b) the shortest distance from Q to PS
Solution:
PQ= 5cm, QR=3cm,RS=4cm and PS = √74cm,
QS = 3 + 4 = 7 cm
5² + 7² = 74
=> PQ² + QS² = PS²
=> ∠Q = 90°
PR² = PQ² + QR²
=> PR² = 5² + 3²
=> PR² = 34
=> PR = √34 cm
the shortest distance from Q to PS would be perpendicular distance
Area of ΔPQS = (1/2) PQ * QS
= (1/2) * 5 * 7
Area of ΔPQS = (1/2) * PS * Height
= (1/2) * √74 * ( the shortest distance from Q to PS)
Equating Both
(1/2) * √74 * ( the shortest distance from Q to PS) = (1/2) * 5 * 7
=> the shortest distance from Q to PS = 35/√74 cm
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