Question

In a triangle pqr angle qpr=90 pq=24cm and qr=26 and in triangle pkr anglepkr=90 kr=8 find pk

Answer 1

pk = 6 units...i calculated and solution is given in the pic plz look it

Answer 2

The length of PK is 6 cm.

Step-by-step explanation:

We are that in a triangle PQR;  $\angle$QPR = 90°, PQ = 24 cm and QR = 26 cm and in triangle PQR; $\angle$PKR = 90° and KR = 8 cm.

As it is given that one angle of the triangle is 90°, this means both the triangles are right-angled triangle.

Firstly, we will find the side PR in the triangle PQR using the Pythagoras theorem.

Pythagoras theorem states that;

$\text{Hypotenuse}^{2} = \text{Perpendicular}^{2} + \text{Base}^{2}$

$\text{QR}^{2} = \text{QP}^{2} + \text{PR}^{2}$

$\text{26}^{2} = \text{24}^{2} + \text{PR}^{2}$

$\text{PR}^{2} = \text{26}^{2}-\text{24}^{2}$

$\text{PR}^{2} = 100$

$\text{PR} = \sqrt{100}$ = 10 cm

Similarly, in the triangle PKR;

$\text{Hypotenuse}^{2} = \text{Perpendicular}^{2} + \text{Base}^{2}$

$\text{PR}^{2} = \text{PK}^{2} + \text{KR}^{2}$

$\text{10}^{2} = \text{PK}^{2} + \text{8}^{2}$

$100 = \text{PK}^{2} + 64$

$\text{PK}^{2} = 100 - 64 = 36$

$\text{PK} = \sqrt{36}$ = 6 cm

Hence, the length of the side PK = 6 cm.