Question

Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side? less than 25 / less than or equal to 25 /equal to 25/ more than 25

Answer 1

A. Less than 25.

Explanation:

Let x represent 3rd side of triangle.

We have been given hat two sides of a triangle have lengths 10 and 15.

We will use triangle inequality theorem to find the 3rd side of the triangle. Triangle inequality theorem states that 3rd side of a triangle must be less than the sum of other two sides of triangle.

Using triangle inequality theorem, we can set following inequalities:

`x+10>15`

`x+10-10>15-10`

`x>5`

Therefore, the length of third side should be greater than 5.

`10+15>x`

`25>x`

`x<25`

Therefore, the length of third side should be less than 25 and option A is the correct choice.

Answer 2

The length of the third side of a triangle is always less than the sum of the other two legs. Therefore if we add the two legs we obtain,

leg 1 + leg 2

10 + 15 = 25

Since the sum of the legs is 25, thus, the third leg should be less than 25.