Question

the sides of a triangle are in the ratio 25: 14: 12 and its perimeter 510 find area using heron's formula ​

Answer 1

Answer:

Step-by-step explanation:

Side of triangle are 25x, 14x and 12x

Perimeter = 510 cm

We know that -

2s = a + b + c

510 = 25x + 14x + 12x

510 = 51x

or

51x = 510

x = 510/51

x = 10 cm

Therefore,

25x = 25X10 = 250 cm

14x = 14X 10 = 140 cm

12x = 12 X 10 = 120 cm

Semi perimeter (s) = 510/2 = 255

area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

= $\sqrt{255(255- 250)(255-140)(255-120)}$

=$\sqrt{255(5)(115)(135)}$ = $\sqrt{255X5X115X135}$

= $\sqrt{19794375}$