Question

the perimeter of triangular field is 300 cm and sides are in ratio of 5:12:13. find the length of perpendicular from the length opposite vertex to the side whose length is 130cm (class-9) need method of the following sum

Answer 1

Hi there!

Your Answer :- 46.15 cm

Let the sides be 5x, 12x, 13x.

So,

$\sf\red{5x + 12x + 13x = 300}$

$\sf\gray{30x = 300}$

$\sf\blue{x = 10}$

So,

5x = 50.

12x = 120.

13x = 130.

We can apply Heron's Formula.

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

Here,

a = 50, b = 120 and c = 130.

First we will calculate Semi Perimeter.

$\sf\purple{s = \dfrac{50 + 120 + 130}{2} = 150}$

$\sf\orange{\sqrt{150(150 - 50)(150 - 120)(150 - 130)} }$

$\sf\pink{3000 \: c {m}^{2} }$

Area of Triangle:-

$\sf\red{\dfrac{1}{2} \times130 \times Height = 3000}$

$\sf\blue{Height \: = \dfrac{3000 \times 2}{130} = 46.15 \: cm}$