contestada

In the diagram below, TU is parallel to Q R. If
RU = 12, TU = 25, and QR = 40, find the length of
SU. Figures are not necessarily drawn to scale. State
your answer in simplest radical form, if necessary.

Respuesta :

akposevictor

Given that ΔQSR and ΔTSU are similar triangles, therefore, the length of SU is: 20.

Recall:

  • When two triangles are similar, the ratio of their corresponding side lengths are equal.

Thus, given the figure attached below, ΔQSR and ΔTSU are similar to each other.

  • Therefore:

SR/SU = QR/TU

SR = RU + SU = 12 + SU

SU = ?

QR = 40

TU = 25

Plug in the values

[tex]\frac{12 + SU}{SU} = \frac{40}{25}[/tex]

  • Cross multiply

[tex](12 + SU)25 = 40(SU)\\\\300 + 25SU = 40SU\\\\300 = 40SU - 25SU\\\\300 = 15SU\\\\\mathbf{SU = 20}[/tex]

Learn more about similar triangles on:

https://brainly.com/question/11850540

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