Question

Angle WXY is an isosceles triangle with WX not equal to 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.

X=
WX=
XY=
WY=

Answer 1

To find x and the measure of each side of the isosceles triangle WXY, we set up equations based on the given information. Solving these equations gives us x = 23, WX = 95, XY = 108, and WY = 95.

Step-by-step explanation:

To find the value of x and the measure of each side of the isosceles triangle WXY, we need to set up an equation based on the given information.

Let x represent the value we are looking for.

Given that WX is 3 more than four times x, we can write the equation: WX = 4x + 3.

XY is 7 less than five times x, so XY = 5x - 7.

And WY is 66 less than seven times x, so WY = 7x - 66.

Since angle WXY is an isosceles triangle, it means that WX = WY. So we can set up an equation: 4x + 3 = 7x - 66.

Solving this equation will give us the value of x, and then we can substitute it back into the equations to find the measures of each side of the triangle.

Let's solve the equation: 4x + 3 = 7x - 66.

Subtracting 4x from both sides, we get 3 = 3x - 66.

Adding 66 to both sides, we obtain 69 = 3x.

Dividing by 3, we find x = 23.

Now we can substitute x = 23 into the three equations to find the measures of each side:

WX = 4(23) + 3 = 92 + 3 = 95.

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

WY = 7(23) - 66 = 161 - 66 = 95.

Therefore, x = 23, WX = 95, XY = 108, and WY = 95.