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In ΔPRQ, the midsegment XY¯¯¯¯¯ is 4 units long. What is the length of QR¯¯¯¯¯?

8 units

4 units

10 units

16 units

In ΔPRQ the midsegment XY is 4 units long What is the length of QR 8 units 4 units 10 units 16 units class=

Respuesta :

calculista

In this problem we have that

XY is parallel to QR

triangle PQR is similar to triangle PXY

[tex]PY=YR \\PX=XQ[/tex]

so

by proportion

[tex]\frac{QR}{XY}= \frac{PR}{PY}[/tex]

we have

[tex]XY=4\ units[/tex]

[tex]PR=2PY\ units[/tex]

substitutes

[tex]\frac{QR}{4}=\frac{2PY}{PY}[/tex]

[tex]\frac{QR}{4}=2[/tex]

[tex]QR=8\ units[/tex]

therefore

the answer is

[tex]8\ units[/tex]

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