Question

Triangle WXY is an isosceles triangle with WX congruent 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.

Answer 1

Applying the definition of isosceles triangle, the value of x = 23.

WX = 95 units; XY = 108 units; WY = 95 units.

What is an Isosceles Triangle?

An isosceles triangle, like triangle WXY that is shown in the image attached below, has two equal sides.

Given the following measures:

• Side WX = 4x + 3
• Side XY = 5x - 7
• Side WY = 7x - 66

Side WX = side WY

Substitute

4x + 3 = 7x - 66

Combine like terms

4x - 7x = -3 - 66

-3x = -69

x = 23

Find each side length by substituting the value of x:

Side WX = 4x + 3 = 4(23) + 3 = 95 units

Side XY = 5x - 7 = 5(23) - 7 = 108 units

Side WY = 7x - 66 = 7(23) - 66 = 95 units

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