Q.3 In a right triangle PQR , angle Q is right angle . If PQ =4 and PR = 5 , find the value of QR.
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Q.3 In a right triangle PQR , angle Q is right angle . If PQ =4 and PR = 5 , find the value of QR.
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Step-by-step explanation:
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Question:
In a Right Triangle PQR, angle Q is right angle. If PQ= 4 and PR= 5, find the value of QR.
Given:
To Find:
Formula to be used:
[tex]\sf{~~~~Pythagoras\: Theorem-{Hypotenuse}^{2}={Base}^{2}+{Height}^{2}} [/tex]
Solution:
Here, PQ is Height of the triangle and PR is hypotenuse of triangle. We have to find value of QR that is base of the triangle. Substituting all the values in Formula (Pythagoras Theorem). We get,
[tex]\rightarrow\mathsf{{Hypotenuse}^{2}={Base}^{2}+{Height}^{2}} [/tex]
[tex]\rightarrow\mathsf{{PR}^{2}={QR}^{2}+{PQ}^{2}} [/tex]
[tex]\rightarrow\mathsf{{5}^{2}={QR}^{2}+{4}^{2}} [/tex]
[tex]\rightarrow\mathsf{{QR}^{2}={5}^{2}-{4}^{2}} [/tex]
[tex]\rightarrow\mathsf{{QR}^{2}=25-16} [/tex]
[tex]\rightarrow\mathsf{{QR}^{2}=9} [/tex]
[tex]\rightarrow\mathsf{QR=\sqrt{9}} [/tex]
[tex]\rightarrow\mathsf{QR=3} [/tex]
Hence, the Length of QR is 3.