Chapter 12.1, Problem 39E

To determine

To find: the two ways that could complete the triangle.

Answer to Problem 39E

The person could make bend $6$ inches from the first bend and leave the last side $8$ inches long or

The person could make another bend of $7$ inches from the first bend and then the last side will also be $7$ inches.

Explanation of Solution

Given:

The strip metal is $20$ inches.

Strip metal is bent to an isosceles triangle.

The first bend is $6$ inches.

Concept used:

Isosceles triangle has two side same.

Sum of the three angles of triangle is always ${180}^0$ .

If the triangle is right triangle then other two angles other than ${90}^0$ will be less than ${90}^0$ .

Calculation:

The two congruent sides could have length $6$ .

  $\begin{array}{l}6+6+b=20.\\ 12+b=20.\\ b=8.\end{array}$

Base is $8$ if other two similar line length is $6$ .

If the one non-congruent side or the base could have length $6$ then:

  $\begin{array}{l}6+l+l=20.\\ 6+2l=20.\\ 2l=14.\\ l=7.\end{array}$

Two similar lines length are $7,7$ if base length is $6$ .

Hence, the person could make bend $6$ inches from the first bend and leave the last side $8$ inches long or

The person could make another bend of $7$ inches from the first bend and then the last side will also be $7$ inches.