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Chapter 6: Q14. (page 221)

The base of an isosceles triangle has length 12. What can you say about the length of a leg?

Short Answer

Expert verified

Leg of the isosceles triangle must have length in between 6 and 18.

Step by step solution

01

Step 1. Apply the concept of isosceles triangle.

An isosceles triangle is a triangle that has two sides of equal length.

Any leg of a triangle must be less than the sum of two sides of triangle.

02

Step 2. Step description.

Consider that an isosceles triangle ABC as below:

Draw a perpendicular from point A.

Thus, AD bisect the base BC.

CD=6

Thus, the leg of the isosceles triangle must be greater than 6.

03

Step 3. Step description.

Also, any leg of a triangle must be less than the sum of two sides of triangle.

Therefore,

AC<6+12AC<18

Hence the leg of the isosceles triangle must be in between 6 and 18

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