Chapter 2.1, Problem 33E

a.

To determine

To find: the dimension of each triangle.

Answer to Problem 33E

6 units, 6 units, 8 units

Explanation of Solution

Given information:

The perimeter of the each triangle (P) is 20 units

Let the length of equal sides be a and length of other side be b.

The dimensions of first triangle (i.e. isosceles triangle) are $a,a$andb.

The dimensions of second triangle are $a,b$ and 6 units.

Calculation:

The perimeter of isosceles triangle will be as follows:

  $P=2a+b$

Put the value of P and rearrange the equation as follows:

  $\begin{array}{l}20=2a+b\\ b=20-2a\text{ [Rearranged to get the value of }b\text{]}\end{array}$

The perimeter of second triangle is as follows:

  $P=a+b+6$

Put the value of P and b and solve the equation as follows:

  $\begin{array}{c}20=a+\left(20-2a\right)+6\\ 20=-a+26\text{ [Solve to get the value of }a\text{]}\\ 20+a=26\\ a=26-20\\ =6\end{array}$

Put the value of a in the rearranged equation for isosceles triangle and evaluate b as shown below.

  $\begin{array}{c}b=20-2a\\ =20-2\left(6\right)\\ =20-12\\ =8\end{array}$

The dimensions of first triangle $\left(a,a,b\right)$ are 6 units, 6 units and 8 units.

The dimensions of second triangle $\left(a,b\text{ and 6 units}\right)$ are 6 units, 8 units and 6 units.

Thus, the dimension for both the triangles is same.

b.

To determine

the type of second triangle.

Answer to Problem 33E

Isosceles triangle

Explanation of Solution

Given information:

The dimensions of second triangle are $a,b$ and 6 units.

Calculation:

The dimensions of second triangle $\left(a,b\text{ and 6 units}\right)$ are 6 units, 8 units and 6 units.

Since, the two sides of the triangle are equal, so it is an isosceles triangle.