Question

Given: PQ ⊥ QR , PR=20, SR=11, QS=5 Find: The value of PS.

Answer 1

Please find the diagram in the attachment for a better understanding of the solution provided here.

We will use the Pythagoras' Theorem here. The right triangle is PQR. Because it is a right triangle, therefore, we can use the Pythagoras' Theorem here.

`PQ=√(PR^2-QR^2)=√(20^2-11^2)=√(400-121)=√(279)\approx 16.7`

Thus, as required by you we have successfully proven that the value of PQ=16.7

Answer 2

PS = 13

Explanation:

QR = QS + SR = 5 + 11 = 16

From Pythagorean theorem

`PQ^2 + QR^2 = PR^2`

Solving for PQ

`PQ = √(PR^2 - QR^2)`

`PQ = √(20^2 - 16^2)`

`PQ = 12`

From Pythagorean theorem

`PQ^2 + QS^2 = PS^2`

Solving for PS

`PS = √(PQ^2 + QS^2)`

`PS = √(12^2 + 5^2)`

`PS = 13`