Question

the sides of triangle are in ratio 5:12:13 and its perimeter is 150m. find the area of triangle.
By heron's formula

Answer 1

$\textbf{ \underline{ Hello Mate! }}$

Let each variable of triangle be x.

Then sides will be = 5x, 12x and 13x

Perimter of ∆ = Sum of all sides

5x + 12x + 13x = 150 m

30x = 150 m => x = 5 m

Sides will be ; 5 × 5 m = 25 m
12 × 5 m = 60 m
13 × 5 m = 65 m

Area of triangle by herons formula that is

$\sqrt{s(s - a)(s - b)(s - c)} \\ where \: s \: = \frac{a + b + c}{2} \\ s = \frac{150}{2} m = 75 \: m \\ = \sqrt{75(75 - 60)(75 - 65)(75 - 25)} \\ = \sqrt{13 \times 5 \times 3 \times 5 \times 2 \times 5 \times 2 \times {5}^{2} } \\ = 5 \times 5 \times 2 \times \sqrt{13 \times 5 \times 3} \\ = 50 \sqrt{195} {m}^{2} \\ = 50 \times 13.96 = 698 \: {m}^{2}$

$\boxed{ Area\:of\:triangle\:is\:698\:m^2 }$

Have great future ahead!

Answer 2

Let the 1st side of the triangle = 5x

the 2nd side of the triangle =12x

the 3rd side of the triangle = 13x

Then ,

According to the question,

5x + 12x + 13x = 150

30x = 150

So, x= 150/30

=5

Hence, the 1st side of the triangle = 5×5=25

the 2nd side of the triangle = 12×5=60

the 3rd side of the triangle = 13×5=65

Since, the triangle is a right triangle

= 5² +12² =13²

25+144=169

169=169

So, the Area of the triangle = 1/2×b×h

= 1/2 ×25× (60)

= 750 m²