Chapter 8, Problem 12CUR

a.

To determine

To check: whether the given $\Delta$

XYZ is scalene, isosceles, or equilateral.

Answer to Problem 12CUR

Isosceles.

Explanation of Solution

Given information: In $\Delta$XYZ, $m\angle X:m\angle Y:m\angle Z=3:3:4$ .

Calculation:

In $\Delta$XYZ, let us say $m\angle X=3x$ , $m\angle Y=3x,m\angle Z=4x$ .

Now, the summation of all the angles in a tringle must be $180°$ .

So, $m\angle X+m\angle Y+m\angle Z=3x+3x+4x=180°$ ,

  $\Rightarrow x=18°.$

Therefore, $m\angle X=54°,m\angle Y=54°,\text{ and }m\angle Z=72°$ .

Now, as the two angles are equal for a tringle, the triangle is isosceles triangle.

b.

To determine

To check: whether the given $\Delta$

XYZ is acute, right, or obtuse.

Answer to Problem 12CUR

Acute.

Explanation of Solution

Given information: In $\Delta$XYZ

  $m\angle X:m\angle Y:m\angle Z=3:3:4$ .

Calculation:

In $\Delta$XYZ from the subpart − a, m:math>m∠X=54°, m∠Y=54°, m∠Z=72° .

Since all the angles are less than $90°$ , the tringle is an acute triangle.

c.

To determine

the longest side of $\Delta$

XYZ .

Answer to Problem 12CUR

XY is the longest side.

Explanation of Solution

Given information: In $\Delta$XYZ

  $m\angle X:m\angle Y:m\angle Z=3:3:4$

Calculation:

In $\Delta$XYZ from above sub − parts, m:math>m∠X=54°, m∠Y=54°, m∠Z=72° .

Since the angle $\angle Z=72°$ is the largest, side $XY$ is the longest.