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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

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 class=

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cryssatemp

1) An Isosceles triangle has three sides, in which two sides are of the same length and the third has a different length. It has two angles of the same value and a third angle with a different value, as well.



In the figure is shown that angles Y and Z are the same, then the sides of this angles must be of the same length. This means that:


XY=XZ

(9n+12)ft=(15n-6)ft      



From this equation we have to find n:


9n-15n=-6-12


-6n=-18


[tex]n=\frac{-18}{-6}[/tex]    

n=3

2) The measure of the leg XY in ft



XY=(9n+12)ft



Substitute the value of n calculated in the first question:


XY=(9(3)+12)ft


XY=39 ft



3) The measure of the leg XZ in ft


XZ=(15n-6)ft


Substitute the value of n calculated in the first question:


XZ=(15(3)-6)ft



XZ=39ft

A triangle is isosceles triangle when the two sides and two angle of the triangle in equal in measure.

  • a) the value of n is 3 units.
  • b) the measure of leg XY is 39 feet.
  • c)the measure of  leg XZ is 39 feet.

What is isosceles triangle?

A triangle is isosceles triangle when the two sides and two angle of the triangle in equal in measure.

Given information-

The length of the side [tex]XY[/tex] is ([tex]9n+12[/tex]).

The length of the side [tex]XZ[/tex] is ([tex]15n-6[/tex]).

The measure of angle,

[tex]m\angle Y=m\angle Z[/tex]

  • a) the value of n-

For the isosceles triangle, the two sides and two angle of the equal in measure.

As the measure of angle,

[tex]m\angle Y=m\angle Z[/tex]

Thus the opposite side of this angles must be equal. Thus,

[tex]XY=XZ[/tex]

Put the values as,

[tex]9n+12=15n-6\\15n-9n=12+6\\6n=18\\n=3[/tex]

Hence the value of n is 3 units.

  • b) the measure of leg XY

The length of the side [tex]XY[/tex] is ([tex]9n+12[/tex]).

Put the value of n,

[tex]XY=9n+12\\XY=9\times3+12\\XY=27+12\\XY=39 \rm ft[/tex]

Hence the measure of  leg XY is 39 feet.

  • c) the measure of leg XZ

The length of the side [tex]XZ[/tex] is ([tex]15n-6[/tex]).

Put the value of n,

[tex]XZ=15n-6\\XZ=15\times3-6\\XZ=39\rm ft[/tex]

Hence the measure of  leg XZ is 39 feet.

  • a) the value of n is 3 units.
  • b) the measure of leg XY is 39 feet.
  • c)the measure of  leg XZ is 39 feet.

Learn more about the isosceles triangle here;

https://brainly.com/question/1475130

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