If PQR is a triangle such that PQ=15 cm, PR=15 cm, QR=18 cm, then altitude to side PR will be

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24 Aug 2022 Geometry

If PQR is a triangle such that PQ=15 cm, PR=15 cm, QR=18 cm, then altitude to side PR will be

OPtion

1) 29 cm
2) 15 cm
3) 14.5 cm
4) 25.4 cm
5) 21.6 cm
6) 20.4 cm
7) 14.4 cm
8) 12.5 cm
9) Cann't be determined
10) None of these

Solution

As two sides PQ, PR are same, it is an isosceles triangle, so altitude to QR will also be perpendicular bisector of QR.
Let PS be the bisector of QR, then QS=SR=9 cm.
By Pythagoras theorem, PS² + SR² = PR²
PS² = 15² - 9² = 144
PS = 12
Now, Area of the triangle = (1/2)* base*height = (1/2)*QR*PS = (1/2)*18*12 = 108 cm²
As we have to find the altitude to PR, Area=(1/2)*PR*(Altitude to PR, say h)
108 = (1/2)*15*h
h = 14.4 cm
Correct Option 7)

Correct Option: 7 Best Solution (1)

RAMADURAI NATESAN   2 years AGO

let altitude to side PR meet PR at S , forming 2 rt.angled Triangles PQS and. RQS.
RS^2 +QS^2 = 324 AND PS^2 + QS^2 = 225.
RS^2 - PS^2 = 99= (RS + PS )(RS - PS) = 15 ( RS - PS).
RS - PS = 6.6. RS = 10.8 QS^2 = 324 - (10.8)^2 = 207.36.
Q = 14.4

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