Question

the perimeter of a triangle is 300 M and its sides are in the ratio 5: 12: 13 find its area​

Answer 1

Answer:

Given that ;

Perimeter of the Triangle ( P ) = 300 m

Ratio of it's Sides are ;

5 : 12 : 13

Let ,

The sides be x

Sides of the Triangle = 5x , 12x , 13x

Formula :

Perimeter of the Triangle ;

( P ) = Sum of all the sides

P = 5x + 12x + 13x

300m = 30x

30x = 300m

x = 300 / 30

x = 10 m

Hence ;

Sides of the Triangle are ,

5x = 5 ( 10 ) = 50m

12x = 12 ( 10 ) = 120m

13x = 13 ( 10 ) = 130m

Answer 2

☘️ Answer :

• Area of triangle = 3000 cm²

☘️ Solution :

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

We know that,

Perimeter = sum of all sides

➪ 300 = 5x + 12x + 13x

➪ 300 = 30x

➪ 300/30 = x

➪ 10 = x

.°. x = 10

So, the sides of the triangle are:

• 5x = 5(10) = 50 m
• 12x = 12(10) = 120 m
• 13x = 13(10) = 130 m

Using Heron's Formula:

$\rm \: s = \dfrac{a + b + c}{2} \\ \\ \sf \: s = \frac{50 + 120 + 130}{2} \\ \\ \sf s = \frac{300}{2} \\ \\ \rm \underline{\: s = 150 \: m}$

.

So,

$\tt Area \: = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \tt \: Area = \tt \sqrt{150(150 - 50)(150 - 120)(150 - 130)} \\ \\ \tt \: Area = \sqrt{150 \times 100 \times 30 \times 20} \\ \\ \tt \underline {\underline{ Area \: = 3000 \: cm {}^{2} }}$

.°. The area of the triangle is 3000 cm².