Mathematics: Which of the following statements must be true of this triangle? A. PR + RQ = PO B. PR + PQ = QR C. PQ + QR - PR D. None of the above are true.

He would take 63minutes to run 6 miles...

Which of the following statements must be true

Quanashiar

21.01.2022

PQ^2+QR^2=PR^2

Step-by-step explanation:

The picture of the question in the attached figure

we know that

In the right triangle PQR of the figure

Applying the Pythagorean Theorem

PR^2=PQ^2+QR^2

Remember that the area of square is equal to

A=b^2

where

b is the length side of the square

Area of square C

A_c=PR^2

$A_c=25\ units^2$ ---> is given

$PR^2=25\ units^2$

Area of square A

A_a=PQ^2

$A_a=9\ units^2$ ---> is given

$PQ^2=9\ units^2$

Area of square B

A_b=QR^2

$A_b=16\ units^2$ ---> is given

$QR^2=16\ units^2$

substitute the given values in the Pythagorean Theorem

PR^2=PQ^2+QR^2

25=9+16

25=25 ---> is true

The Pythagorean Theorem is satisfied (PQR is a right triangle)

we have

PR^2=PQ^2+QR^2

rearrange

PQ^2+QR^2=PR^2

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