Question

In isosceles triangle WXY, XY is 13 inches in length and WY is 10 inches. What is the length of XZ? answer asap please

Answer 1

Answer:  12 inches

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Explanation:

Notice the double tickmarks on segments WZ and ZY. This tells us the two segments are the same length. Let's say they are m units long, where m is a placeholder for a positive number.

That would mean m+m = 2m represents the length of segment WY, but that's equal to 10 as the diagram shows. We have 2m = 10 lead to m = 5 after dividing both sides by 2.

We've shown that WZ and ZY are 5 units long each. In short, we just cut that length of 10 in half.

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Let's focus on triangle XYZ. This is a right triangle with legs XZ = unknown and ZY = 5. The hypotenuse is XY = 13.

We'll use the pythagorean theorem to find XZ

a^2 + b^2 = c^2

(XZ)^2 + (ZY)^2 = (XY)^2

(XZ)^2 + (5)^2 = (13)^2

(XZ)^2 + 25 = 169

(XZ)^2 = 169-25

(XZ)^2 = 144

XZ = sqrt(144)

XZ = 12

Segment XZ is 12 inches long.