Question

Find the area of triangle whose side are in the ratio 5:12:13 and its perimeter is 60cm

Answer 1

Let the sides be 5x,12x,13x
Then,
5x+12x+13x=60
= 30x=60
= x= 60/30= 2cm
.°. Sides are=
5×2=10cm
12×2=24cm
13×2=26cm
.°.it is a right angled triangle
.°. Area= 1/2×10×24 = 120cm^2

Answer 2

$\huge\sf{Answer}$

Given

• Ratio of sides of a triangle = 5 : 12 : 13

• Perimeter = 60cm

To find

• Area of triangle

Let the constant ratio be x

Sides of the triangle :

a = 5x

b = 12x

c = 13x

Given perimeter = 60 cm

Semi perimeter of the triangle s = (a + b + c)/2

⇒ s = (5x + 12x + 13x)/2

⇒ s = 30x/2

⇒ s = 15x

Also, s = Perimeter/2 = 60/2 = 30 cm

⇒ s = 30

⇒ 15x = 30

⇒ x = 30/15 = 2

Sides of the triangle :

a = 5x = 5 * 2 = 10 cm

b = 12x = 12 * 2 = 24 cm

c = 13x = 13 * 2 = 26 cm

Semi perimeter s = 15x = 15 * 2 = 30 cm

By using Heron's formula

Area of the triangle A = √[ s(s - a)(s - b)(s - c)

Substituting the value,

⇒ A = √[ 30(30 - 10)(30 - 24)(30 - 26) ]

⇒ A = √[ 30(20)(6)(4) ]

⇒ A = √14400

⇒ A = 120 cm²

Hence, area of the triangle is 120 cm².

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