Question

Q.3 In a right triangle PQR , angle Q is right angle . If PQ =4 and PR = 5 , find the value of QR.​

Answer 1

Step-by-step explanation:

this is the answer of this question

Answer 2

Question:

In a Right Triangle PQR, angle Q is right angle. If PQ= 4 and PR= 5, find the value of QR.

Given:

• PQR is a right-angled triangle, with Q right angled.
• Length of PQ is 4
• Length of PR is 5

To Find:

• Length of QR

Formula to be used:

$\sf{~~~~Pythagoras\: Theorem-{Hypotenuse}^{2}={Base}^{2}+{Height}^{2}}$

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,

$\rightarrow\mathsf{{Hypotenuse}^{2}={Base}^{2}+{Height}^{2}}$

$\rightarrow\mathsf{{PR}^{2}={QR}^{2}+{PQ}^{2}}$

$\rightarrow\mathsf{{5}^{2}={QR}^{2}+{4}^{2}}$

$\rightarrow\mathsf{{QR}^{2}={5}^{2}-{4}^{2}}$

$\rightarrow\mathsf{{QR}^{2}=25-16}$

$\rightarrow\mathsf{{QR}^{2}=9}$

$\rightarrow\mathsf{QR=\sqrt{9}}$

$\rightarrow\mathsf{QR=3}$

Hence, the Length of QR is 3.