Question

sides of a triangle are in the ratio of 12: 17:25 and its perimeter is 540 cm. find its area

Answer 1

Add the ratios which is 54 then divide it by the perimeter to find the exact sides of each triangle, 540 / 54 = 10, the, multiply 10 to each ratio, that is the sides are 120, 170 and 250. To find the area you must use Heron’s Formula since you only have sides.

Where semiperimeter or s =a + b + c /2 where a,b and c are the sides.

Then substitute it to sqrt s(s-a)(s-b)(s-c) = Area of Triangle

S= 120+170+250=540/2=270

Then.. sqrt 270(150)(100)(20) = 9000 = Area
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Answer 2

Let the sides be 12x,17x and 25x.
now perimeter=540cm
so 12x+17x+25x=540
54x=540x
x=10
so the sides are 120,170,250

s(semi perimeter )=perimeter/2
s=540/2
s=270

area of scalene triangle=√s×(s-a)×(s-b)×(s-c). where a, b, c are the sides
area=√270×150×100×20
=√2×3×3×3×5×2×5×3×5×2×5×2×5×2×2×5
=2×3×5×3×5×2×5×2
=9000cm^2
so the area is 9000 CM square
☺️HOPE IT HELPS☺️
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