Question

Use the given figure and find the length of TU. please help me out.

Answer 1

The length of TU is 8 units.

Explanation:

In triangle XST and triangle XUT,

`\angle SXT=\angle UXT` (Given)

`\angle XST=\angle XUT=90^(\circ)` (Given)

`\angle XT=\angle XT` (Common side)

By AAS postulate,

`\triangle XST\cong \triangle XUT`

Now,

`\angle ST=\angle UT` (CPCTC)

`3x+2=7x-6`

`8=4x`

`2=x`

The value of x is 2.

`TU=7x-6`

`TU=7(2)-6`

`TU=8`

Therefore the length of TU is 8 units.