Question

. The sides of a triangle are in the ratio 5:12:13f its perimeter is 90 cm, find the area of the
triangle.
​

Answer 1

Answer:

5x=15

12x=36

13x=39

Step-by-step explanation:

5x+12x+13x=90

x=90/30

x=3

5²+12²=13²

as this statement shows it is a phythagoran

triplet.

:. area of the ∆ is 5×12=60

mark plz.........

Answer 2

Given

The sides of a triangle are in the ratio 5:12:13 its perimeter is 90 cm

To Find

Area of the triangle

Solution

Let ,

Sides be 5x , 12x , 13x respectively

We know that , " Perimeter is equals to sum of all sides "

Given  , Perimeter = 90 cm

⇒ 5x + 12x + 13x = 90

⇒ 30x = 90

⇒ x = 3 cm  $\green{\bigstar}$

1st side , 5x = 15 cm

2nd side , 12x = 36 cm

3rd side , 13x = 39 cm

Apply Herons formula for finding the area of the triangle .

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

where ,

• a = 15 cm
• b = 36 cm
• c = 39 cm
• s = $\rm \dfrac{a+b+c}{2}=\dfrac{90}{2}=45\ cm$

Apply formula ,

$\to \rm \sqrt{s(s-a)(s-b)(s-c)}\\\\\to \rm \sqrt{45(45-15)(45-36)(45-39)}\\\\\to \rm \sqrt{45(30)(9)(6)}\\\\\to \rm \sqrt{5\times 9\times 5\times 6\times 9\times 6}\\\\\to \rm 5\times 9\times 6\\\\\to \bf \pink{270\ cm^2\ \; \bigstar}$

So , Area of the triangle = 270 cm²