contestada

WXY is an isosceles triangle with line WX congruent to line WY. if WX is 3 more than four times x, XY is 7 less than five times x, and WY is 66 less than seven times x, find x and the measure of each side.

Respuesta :

emclark041

Answer:

x=10

Step-by-step explanation:

part 1:

4x+3=5x-7

(subtract 4x from 5x to get 1x and add 7 to 3 to get 10)

1x=10

x=10

part 2:

WX=4(10)+3=43

XY=5(10)-7=43

WY=7(10)-66=4

MrRoyal

An isosceles triangle, have two congruent sides.

  • The value of x is 23
  • The measure of each side is 95, 95 and 108

From the question, we have the following highlights

[tex]\mathbf{WX = WY}[/tex]

[tex]\mathbf{WX = 3 + 4x}[/tex]

[tex]\mathbf{XY = 5x - 7}[/tex]

[tex]\mathbf{WY = 7x - 66}[/tex]

(a) Find x

We have:

[tex]\mathbf{WX = WY}[/tex]

Substitute values for WX and WY

[tex]\mathbf{3 + 4x = 7x - 66}[/tex]

Collect like terms

[tex]\mathbf{7x - 4x = 3 + 66}[/tex]

[tex]\mathbf{3x = 69}[/tex]

Divide both sides by 3

[tex]\mathbf{x = 23}[/tex]

Hence, the value of x is 23

(b) The measure of each side

Substitute 23 for x in:

[tex]\mathbf{WX = 3 + 4x}[/tex]

[tex]\mathbf{XY = 5x - 7}[/tex]

[tex]\mathbf{WY = 7x - 66}[/tex]

[tex]\mathbf{W = 3 + 4 \times 23}[/tex]

[tex]\mathbf{W = 95}[/tex]

[tex]\mathbf{XY = 5x - 7}[/tex]

[tex]\mathbf{XY = 5 \times 23 - 7}[/tex]

[tex]\mathbf{XY = 108}[/tex]

[tex]\mathbf{WY = 7x - 66}[/tex]

[tex]\mathbf{WY = 7 \times 23 - 66}[/tex]

[tex]\mathbf{WY = 95}[/tex]

Hence, the measure of each side is 95, 95 and 108

Read more about isosceles triangles at:

https://brainly.com/question/2456591

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