The lengths of the sides of a triangle are in the ratio 5 : 6 : 7. Describe the length of the longest side if the perimeter is less than 54 cm.

Solution:

Given,ratio of the lengths of the sides of a triangle = 5 : 6 : 7

Perimeter is less than 54cm.

Let the three sides of the triangle be a, b and c.

So, a:b:c = 5:6:7

Total ratio = 5 + 6 + 7 = 18

Perimeter < 54

We have to find the length of the longest side of the triangle.

From the given ratio, c is the longest side

So, c < (7/18)(54)

c < 7(3)

c < 21cm

Therefore, the length of the longest side is less than 21 cm.

The lengths of the sides of a triangle are in the ratio 5 : 6 : 7. Describe the length of the longest side if the perimeter is less than 54 cm.

Summary:

The lengths of the sides of a triangle are in the ratio 5 : 6 : 7. If the Perimeter is less than 54 cm, then the length of the longest side is less than 21cm.