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Sides of a triangle are in a ratio of 12:17:25 and its perimeter is 540 cm. Find its area by heron's formula?
Most Upvoted Answer
Sides of a triangle are in a ratio of 12:17:25 and its perimeter is 54...
Perimeter= 540cm ; a:b:c= 12:17:25
Let, a= 12x
b= 17x
c= 25x
12x+17x+25x=540
54x=540
x= 540/54
x= 10
Then, a= 12x=12×10=120cm
b= 17x=17×10=170cm
c= 25x=25×10=250cm
By HERON'S FORMULA,
S ( semi perimeter )= a+b+c/2
= 540/2
= 270cm
Area of triangle=√ s (s-a)(s-b)(s-c)
=√270 (270-120)(270-170)(270-250)
=√270×150×100×20
=√2×3×3×3×5×2×3×5×5×2×2×5×5×2×2×5
= 2×3×3×5×3×5×2×5×2
= 9000cm ^2..
Community Answer
Sides of a triangle are in a ratio of 12:17:25 and its perimeter is 54...
Let the common multiple be x
a=12x
b= 17x
c = 25x
perimeter =540 cm
perimeter = a+b+c
540 = 12x+17x 25x
540 = 54x
x = 10 cm

a=120 cm
b= 170 cm
c= 250 cm

semiperimeter = a+b+c/2
= 540/2
= 270 cm


area = 9000 cm²
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Sides of a triangle are in a ratio of 12:17:25 and its perimeter is 540 cm. Find its area by heron's formula?
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