Question

The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?​

Answer 1

Answer:

Ratio of sides = 5:12:13

Perimeter = 300m

So, we have:

5x + 12x + 13x = 300m

30x = 300m

x = 10m

The sides are:

5x = 5 x 10 = 50m

12x = 12 x 10 = 120m

13x = 13 x 10 = 130m

We can solve this two ways.

1st solution:

Clearly, the triangle is a right angled triangle, because:

$13^{2}$ = $12^{2}$ + $5^{2}$

In a right-angled triangle, the legs are the base and height.

So, using 1/2bh,

= 1/2 x 12 x 5

= 30$m^{2}$

2nd solution:

We know the sides, so we can use Heron's formula.

Semiperimeter = (12 + 5 + 13)/2 = 30/2 = 15

So, using heron's formula:

$\sqrt{s(s-a)(s-b)(s-c)}$

=$\sqrt{15 (15-13)(15-12)(15-5)}$

=$\sqrt{15(2)(3)(10)}$

=$\sqrt{900}$

=30$m^{2}$

Hope it helped. Please mark as brainliest.