Question

the side of a triangle are in the ratio 13:14:15 and its perimeter is 84cm . find the area of a triangle.

Answer 1

Hello,

Let the sides of triangle given in ratio be 13x, 14, and 15x.

Given,
Perimeter of Triangle = 84 cm
Sum of all sides if triangle = 84 cm
13x + 14x + 15x = 84 cm
42x = 84 cm
$x = \frac{84 }{42}$

x = 2 cm
Hence,
Sides will be 13×2, 14×2, 15×2 = 26 cm, 28 cm, 30 cm

Semi perimeter of triangle, x =
$\frac{26 + 28 + 30}{2}$

$= \frac{84}{2}$
= 42 cm

Area of triangle,
$\sqrt{x(x - 26)(x - 28)(x - 30)}$
$\sqrt{42(42 - 26)(42 - 28(42 - 30)}$
$\sqrt{42 \times 16 \times 14 \times 12}$
$\sqrt{112896}$
$= 336$
Hence,
The area of triangle = 336 square cm

:)

Answer 2

Heya,

Given:-
Ratio of the sides of the triangle = 13:14:15
Perimeter = 84cm

To find:-
Area

Solution:-
Perimeter = a + b + c
84 = 13x + 14x + 15x
84 = 42x
84/42 = x
42/21 = x
2 = x

Therefore,
Sides:
13x = 13 × 2 =26cm
14x = 14 × 2 = 28cm
15x = 15 × 2 = 30cm

s = P / 2
s = 84/2
s = 42cm

To find area,

Using herons formula,
Area = √ s ( s-a ) ( s-b ) ( s-c )
Area = √42 (42-26)(42-28)(42-30)
Area = √42 × 16 × 14 × 12
Area = √7 × 6 × 4 × 4 × 7 × 2 × 6 × 2
Area = 7 × 6 × 4 × 2
Area = 42 × 8
Area = 336cm^2

Hope my answer helps you :)

Regards,
Shobana
^_^