In a figure , PQR is aright angled triangle , right angled at P. A perpendicular line PS is drawn from P to QR . PR=5 and PQ =12 . What is RS:SQ?
Answers
RS : QS = 25 : 144
Given : PQR is a right-angled triangle, right angled at P
A perpendicular line PS is drawn from P to QR.
PR = 5 cm and PQ = 12 cm
To Find : RS : SQ
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Solution :
Pythagoras' theorem:
Square on the hypotenuse of a right-angled triangle is equal to the
sum of the squares of the other two perpendicular sides.
QR² = PQ² + PR²
=> QR² = 12² + 5²
=> QR² = 13²
=> QR = 13 cm
Area of Triangle = (1/2) x base x height
Area of Δ PQR = (1/2) x PQ x PR
Area of Δ PQR = (1/2) x QR x PS
Equate area
(1/2) x PQ x PR = (1/2) x QR x PS
=> PQ x PR = QR x PS
=> 12 x 5 = 13 x PS
=> PS = 60/13 cm
in ΔPRS
RS² = PR² - PS²
=> RS² = 5² - (60/13)²
=> RS² = (5/13)² (13² - 12²)
=> RS² = (5/13)² (5²)
=> RS = (5/13)5
=> RS = 25/13
in ΔPQS
QS² = PQ² - PS²
=> QS² = 12² - (60/13)²
=> QS² = (12/13)² (13² - 5²)
=> QS² = (12/13)² (12²)
=> QS = (12/13)(12)
=> QS = 144/13
RS : QS = 25 : 144
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