Question

Two sides of a triangle have the measures 7 and 10. Is it true or false that the range of possible measures for the third side is 7

True

False

Answer 1

True

Explanation:

We know that The triangle inequality states that the sum of the two sides of the triangle is always greater than the third side.

Here given that two sides of the triangle are 7 and 10

Let the third side be x

Here a = 7 , b = 10 , c = x

According to the triangle inequality

a + b > c

7 + 10 > x

x < 17

Also c + b > a

x + 10 > 7

x > -3

Also a + c > b

7 + x > 10

x > 3

Combining all the above results we get

3 < x < 17

All the values of x in the above region forms a triangle

Given x values lies in the region so they form a triangle