Question

One side of a triangle is 6 cm shorter than the base, x. The other side is 4 cm longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least 43 cm?

Answer 1

x= base
one side= x-6
other side= 4+x

x+x-6+4+x = 43

3x=43+2

x=15 length of base

Answer 2

The length of the base should be greater or equal to 15 cm or the length of base should be at least 15 cm.

Explanation:

Consider the provided information.

It is given that the base is x cm.

One side of the triangle is 6 cm shorter than the base, this can be written as:

One side = x - 6

The other side is 4 cm longer than the base, this can be written as:

Other side = x + 4

Now it is given that perimeter of the triangle to be at least 43 cm, that means perimeter should be greater than or equal to 43.

Use the inequity ≥ for greater than or equal to.

Perimeter of a triangle is sum of all sides.

x - 6 + x + x + 4 ≥ 43

3x - 2 ≥ 43

3x ≥ 43 + 2

3x ≥ 45

x ≥ 15

Hence, the length of the base should be greater or equal to 15 cm or the length of base should be at least 15 cm.