Question

The perimeter of a triangle is 288m and the ratio of the sides is 3:4:5.Find the area of the triangle.




please bro.​

Answer 1

Step-by-step explanation:

perimeter of a triangle = sum of all sides

288=3x+4x+5x

288=12x

X= 24

the dimensions are 72,96,120

area of a triangle=base × height ÷ 2

= 72.96/2= 3456m^2

Answer 2

Answer :-

Area of triangle is 3456 m²

$\rule{150}2$

The perimeter of the triangle is 288 m (given).

We know that,

$\sf{\bold{Perimeter\:of\:triangle\:=\:Sum\:of\:it's\:sides}}$

A triangle contains three sides. And in question, we also gave its sides in the ratio 3:4:5.

Let the -

• the first side of the triangle be 3x
• the second side of the triangle be 4x
• the third side of the triangle be 5x

So,

Sum of it's (triangle) sides = 3x + 4x + 5x

According to question,

The perimeter of triangle = Sum of all sides of the triangle

Substitute the known values above to find the area of a triangle.

⇒ 288 = 3x + 4x + 5x

⇒ 288 = 12x

⇒ 288/12 = x

⇒ 24 = x

⇒ x = 24

$\implies$ First side of triangle = 3(24)

⇒ 72

$\implies$ Second side of triangle = 4(24)

⇒ 96

$\implies$ Third side of triangle = 5(24)

⇒ 120

Now,

$\sf{\bold{Area \:of\: triangle \:= \:\dfrac{1}{2}\:\times\:base\:\times\:height}}$

Let the -

• base (B) of triangle be 72 m
• height or perpendicular (P) of triangle be 96 m
• hypoteneous (H) of triangle be 120 m

By Pythagoras theorem

→ (H)² = (B)² + (P)²

→ (120)² = (72)² + (96)²

→ 14400 = 5184 + 9216

→ 14400 = 14400

So,

⇒ 1/2 × 72 × 96

⇒ 72 × 48

⇒ 3456 m²