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 54cm.

Answer 1

length of the longest side is less than 21

Explanation:

5n+6n+7n=18n

18n<54

n<54/18

n<3

7*3=21( longest side. )

Answer 2

Less than 21 cm.

Explanation:

Let x represent the multiplier.

We have been given that the lengths of the sides of a triangle are in the ratio 5:6:7. The perimeter of all sides of the triangle would be
`5x+6x+7x`.

We have been given that the perimeter is less than 54 cm.

We can set this information in an inequality as:

`5x+6x+7x<54`

`18x<54`

`(18x)/(18)<(54)/(18)`

`x<3`

Since the length of longest side is
`7x`, so:

`7x<7\cdot 3`

`7x<7\cdot 3`

`7x<21`

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