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Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area.
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find
the area of the triangle.
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Step-by-step explanation:
Q.1. Let the sides be 12x,17x and 25x.
Perimeter= 12x+17x+25x= 54x= 540 cm.
54x=540.
x=10 cm.
Sides are 120, 170 ,250 cm.
Semi perimeter= 270 cm.
Area= √ 270(270-120)(270-170)(270-250)
==> √ 270×150×100×20
==> 10√27×15×2×1000
==> 100√ 3³× 30× 10
==> 300√ 3×3×100
==> 9000 cm².
Q.2.
Let the third side be x m.
Perimeter is 30 cm.
Equal sides are 12 cm.
Perimeter = 12+12+×= 30 cm.
==> 24+x =30
==> x=6 cm.
Area of an isosceles triangle =b/4(√4a²-b²)
==> 6/4 (√4×12×12- 6×6)
==> 2/3 (√576-36)
==> 2/3 (√540)
==> 2/3× 6√15
==> 4√15 cm².
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