Question

In triangle PQR, <Q=90°,PR= 15 cm, PQ= 12 cm, QR=?​

Answer 1

Answer:

Step-by-step explanation:

traingle PQR is right angled at Q

so  using Pythagorus theorum :

PQ² + QR² = PR²

QR² = PR² - PQ²

       = 15² - 12²

       = 225 - 144

QR² = 81

QR =  $\sqrt{81}$

QR = 9cm

Answer 2

★ How to do :-

Here, we are given with two sides of a right-angled triangle. We are asked to find the measurement of the third side of the triangle. Here, we are going to use the concept called as pythagoras theorem which is applicable for only right-angled triangle which has one of the angle measuring 90°. This concept says that the sum of square of other two sides of a right-angled triangle is always equal to the hypotenuse side of a right-angled triangle. So, let's solve!!

$\:$

➤ Solution :-

${\tt \leadsto {PR}^{2} = {PQ}^{2} + {QR}^{2}}$

Substitute the given values.

${\tt \leadsto {15}^{2} = {12}^{2} + {QR}^{2}}$

Find the square numbers of both values.

${\tt \leadsto 225 = 144 + {QR}^{2}}$

Shift the number 144 from RHS to LHS, changing it's sign.

${\tt \leadsto 225 - 144 = {QR}^{2}}$

Subtract the values on LHS.

${\tt \leadsto 81 = {QR}^{2}}$

Apply square root on LHS by removing the square on RHS.

${\tt \leadsto \sqrt{81} = {QR}^{2}}$

Find the square root of 81 to get the final answer.

${\tt \leadsto \pink{\underline{\boxed{\tt {QR}^{2} = 9 cm}}}}$

$\Huge\therefore$ The measurement of QR is 9 cm.

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More to know :-

• Pythagoras theorem is a concept which is used to find any side of a right-angled triangle when two of it's sides are given. It was invented by a mathematician called Pythagoras.
• This property sats that the sum of square of other two sides of a right-angled triangle is always equal to the hypotenuse side of the same triangle.