classyfing triangles

Question

WXY is an isosceles triangle with WX=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.

Answer 1

Hi Melissa J.

WX = WY = 95

XY = 108

In your Isosceles Triangle

WX = WY

WX is 3 more than 4 times x so

WX = 4x + 3

WY is 66 less than 7 times x so

WY = 7x - 66

And XY is 7 less than 5 times x so

XY = 5x - 7

Given the information above we can make the following substitutions

WX = WY

4x + 3 = 7x - 66

Isolate variables on one side of the equation and constants on the other

66 + 3 = 7x - 4x

69 = 3x

Divide both sides by 3 to solve for x

69/3= x

23 = x

Now that we have x we can plug it back in to the equation for the sides of our Isosceles Triangle

4x + 3 = 7x - 66

4(23) + 3 = 7(23) - 66

92 + 3 = 161 - 66

95 = 95

So

WX = WY = 95

XY = 5x - 7

XY = 5(23) - 7 = 115 - 7 = 108

I hope this helps