Question

Wxy is an isosceles triangle with wx congruent to wy if wx is 3 more than 4 times x , xy is 7 less than fivet imes x, and wy is 66 less than seven times x, find x and the measure of each side

Answer 1

The problem involves solving for the sides of an isosceles triangle given expressions in terms of x. By setting the expressions for the congruent sides equal to each other, we solve for x = 23, then find the side lengths: WX = WY = 95, and XY = 108.

Step-by-step explanation:

The student is asking a mathematics problem related to solving for the sides of an isosceles triangle given algebraic expressions for each side in terms of a variable x. To find the length of the sides and the value of x, we set the expressions for the congruent sides equal to each other and solve for x. Since WX is congruent to WY, the equations derived from the given information are as follows:

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

To find x, we set the expressions for WX and WY equal since those are the congruent sides in an isosceles triangle:

3 + 4x = 7x - 66

Solving for x will give us:

66 + 3 = 7x - 4x

69 = 3x

x = 23

With x found, we can now find the measures of each side:

• WX = 3 + 4(23) = 3 + 92 = 95
• XY = 5(23) - 7 = 115 - 7 = 108
• WY = 7(23) - 66 = 161 - 66 = 95

The lengths of the sides of the isosceles triangle are WX = 95, XY = 108, and WY = 95.