Question

The sides of a triangle are in the ratio 4:5:2. Find the sides of triangle, if its perimeter is 660 centimetre(answer 240cm,300cm,120cm)

Answer 1

$\bf{Given \: :}$
The sides of triangle are in ratio 4:5:2,
Perimeter of triangle is 660 cm.

.

Let, sides of triangle be,
a = 4x
b = 5x
c = 2x

We know that,
Perimeter of triangle = sum of all three sides

=> 660 = 4x + 5x + 2x

=> 660 = 11x

=> $\frac{660}{11}$ = x

=> 60 = x

So,

sides of the triangle are,

$\bf{a = 4x = 4×60 = 240 cm}$
$\bf{b = 5x = 4×60 = 300 cm}$
$\bf{c = 2x = 4×60 = 120 cm}$

Answer 2

Since, we are given the ratio of the sides of the triangle, we cannot just use those values in our calculation. For the same reason let us assume the three sides of the triangle as 4x, 5x and 2x.

Also, we are given the perimeter of the triangle i.e. 660 cm

But, perimeter of the triangle is also equal to ( 4x + 5x + 2x ) cm.

Hence,

On relating the two results we can have the following equation,

( 4x + 5x + 2x ) = 660

11x = 660

x = 660 / 11

x = 60 cm

Now based on our assumption we can find the exact values of the three sides of triangle which are as follows:

First Side = 4x = 4 * 60 = 240 cm

Second Side = 5x = 5 * 60 = 300 cm

Third Side = 2x = 2 * 60 = 120 cm