Question

How would I work this out

Answer 1

10.1

Explanation:

You can find the length of XY by first finding YZ using the Pythagorean theorem. Then subtract the length from 15 for the length of the other triangle. Use the Pythagorean theorem again to find XY.

The Pythagorean theorem is used for all right triangles and is the formula
`a^2 + b^2 = c^2`. Here a = 4, b is unknown and c = 7.

So
`4^2 + b^2 = 7^2\\16 + b^2 = 49\\b^2 = 33\\b = √(33) =5.75`

Subtract 5.75 from 15.

15 - 5.75 = 9.25.

Repeat the Pythagorean Theorem again with a = 4, b = 9.25 and c is unknown. Solve for c. This is XY.

`4^2 + 9.25^2 = c^2\\16 + 85.56 = c^2\\101.6 = c^2\\10.1 = c`