Question

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.

Answer 1

Answer:  The longest side of the triangle is less than 21 cm.

Step-by-step explanation:  Given that the lengths of the sides of a triangle are in the ratio 5 : 6 : 7.

We are to describe the length of the longest side if the perimeter is less than 54 cm.  

The perimeter of a triangle is equal to the sum of the lengths of the three sides.

Let 5x, 6x and 7x represents the lengths of the three sides of the triangle. So, we get

$5x+6x+7x$

Therefore, the length of the longest side is given by

$7x$

Thus, the longest side of the triangle is less than 21 cm.

Answer 2

5n+6n+7n=18n

18n<54

n<54/18

n<3

7*3=21 for the longest side.

Thus the longest side is less than 21.

Hope this helps