Question

Find y, ST and TU Please help!

Answer 1

Given:

$ST=4y,TU=2y+6$

To find:

The value of  y, ST and TU.

Solution:

In triangle STV and UTV,

$m\angle TSV\cong n\angle TUV$            (Given right angles)

$m\angle SVT\cong n\angle UVT$            (Given)

$TV\cong TV$            (Common side)

The corresponding two angles and a non included sides in both triangles are congruent. So, the triangles are congruent by using AAS congruence postulate.

$\Delta STV\cong \Delta UTV$           (AAS congruence postulate)

Corresponding parts of congruent triangles are congruent. So,

$ST\cong UT$              (CPCTC)

$4y=2y+6$

$4y-2y=6$

$2y=6$

$y=3$

Now,

$ST=4y$

$ST=4(3)$

$ST=12$

And,

$TU=2y+6$

$TU=2(3)+6$

$TU=6+6$

$TU=12$

Therefore, $y=3,\ ST=12\ units,\ TU=12\ units$.