Question

Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y Z and Y Z X are congruent. Consider isosceles ΔXYZ. What is the value of n? What is the measure of leg XY? ft What is the measure of leg XZ? ft

Answer 1

1st box: 3

2nd box: 39

3rd box: 39

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Answer 2

*the figure is shown in the attachment

Answer/Step-by-step explanation:

Since <XYZ and <YZX are said to be congruent, therefore, the side opposite to each of the angle are also equal. Therefore, ∆XYZ is an isosceles ∆.

Find the value of n by creating an equation to solve for n:

XY = (9n + 12) ft

XZ = (15n - 6) ft

XY = XZ (2 equal lengths of isosceles ∆)

9n + 12 = 15n - 6 (substitution)

Combine like terms

9n - 15n = - 12 - 6

-6n = -18

Divide both sides by -6

-6n/-6 = -18/-6

n = 3

Find the length of leg XY by substituting n = 3 into XY = (9n + 12) ft.

XY = (9(3) + 12) ft

XY = (27 + 12) ft

XY = 39 ft

Find the length of leg XZ by substituting n = 3 into XZ = (15n - 6) ft.

XZ = (15(3) - 6) ft

XZ = (45 - 6) ft

XZ = 39 ft