Respuesta :

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.

[tex]PQ=\sqrt{PR^2-QR^2}=\sqrt{20^2-11^2}=\sqrt{400-121}=\sqrt{279}\approx 16.7[/tex]

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

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Answer:

PS = 13

Step-by-step explanation:

QR = QS + SR = 5 + 11 = 16

From Pythagorean theorem

[tex]PQ^2 + QR^2 = PR^2 [/tex]

Solving for PQ

[tex]PQ = \sqrt{PR^2 - QR^2}  [/tex]

[tex]PQ = \sqrt{20^2 - 16^2}  [/tex]

[tex]PQ = 12 [/tex]

From Pythagorean theorem

[tex]PQ^2 + QS^2 = PS^2 [/tex]

Solving for PS

[tex]PS = \sqrt{PQ^2 + QS^2} [/tex]

[tex]PS = \sqrt{12^2 + 5^2} [/tex]

[tex]PS = 13[/tex]

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