Find y, ST and TU
Please help!

Question

01-04-2021
Mathematics

Answered

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Find y, ST and TU
Please help!

Sagot :

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erinna erinna · Answer 1 · 2021-04-05T21:24:02-04:00

Given:

[tex]ST=4y,TU=2y+6[/tex]

To find:

The value of y, ST and TU.

Solution:

In triangle STV and UTV,

[tex]m\angle TSV\cong n\angle TUV[/tex] (Given right angles)

[tex]m\angle SVT\cong n\angle UVT[/tex] (Given)

[tex]TV\cong TV[/tex] (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.

[tex]\Delta STV\cong \Delta UTV[/tex] (AAS congruence postulate)

Corresponding parts of congruent triangles are congruent. So,

[tex]ST\cong UT[/tex] (CPCTC)

[tex]4y=2y+6[/tex]

[tex]4y-2y=6[/tex]

[tex]2y=6[/tex]

[tex]y=3[/tex]

Now,

[tex]ST=4y[/tex]

[tex]ST=4(3)[/tex]

[tex]ST=12[/tex]

And,

[tex]TU=2y+6[/tex]

[tex]TU=2(3)+6[/tex]

[tex]TU=6+6[/tex]

[tex]TU=12[/tex]

Therefore, [tex]y=3,\ ST=12\ units,\ TU=12\ units[/tex].

Sagot :

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