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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

Respuesta :

MrRoyal

Answer:

[tex]n = 3[/tex]

[tex]XY = 39[/tex]

[tex]XZ = 39[/tex]

Step-by-step explanation:

Given

[tex]XY = 9n + 12[/tex]

[tex]XZ = 15n - 6[/tex]

[tex]<XYZ = <YZX[/tex]

Solving (a): n

To solve for n;

We make use of

[tex]XY = XZ[/tex]

Substitute values for XY and XZ

[tex]9n + 12 = 15n - 6[/tex]

[tex]9n - 15n = -12 - 6[/tex]

[tex]-6n = -18[/tex]

Divide through by -6

[tex]n = 3[/tex]

Solving (b) XY

[tex]XY = 9n + 12[/tex]

Substitute 3 for n

[tex]XY = 9 * 3 + 12[/tex]

[tex]XY = 27 + 12[/tex]

[tex]XY = 39[/tex]

Solving (c): XZ

[tex]XZ = XY[/tex]

[tex]XZ = 39[/tex]

The value of n is 3, the measure of leg XY is 39 ft, and the measure of XZ is 39 ft and this can be determined by using the properties of an isosceles triangle.

Given :

  • 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.

Given that the angle XYZ and angle YZX are congruent to each other and triangle XYZ is an isosceles triangle.

From the above statement, it can be concluded that the side length of XY and the side length of XZ is also congruent to each other, that is:

XY = XZ

9n + 12 = 15n - 6

Simplify the above expression in order to determine the value of 'n'.

18 = 6n

n = 3 ft

The measure of leg XY is given by:

XY = 9(3) + 12 = 39 ft

The measure of leg XZ is given by:

XZ = 15(3) - 6 = 39 ft

For more information, refer to the link given below:

https://brainly.com/question/19237987