Question

Find the length of PR from the given figure ( step by step ). ​

Answer 1

`PR=39`

Explanation:

The triangle (PQR) is a right triangle. This means the triangle has a (90) degree angle, such is indicated by the box around one of the angles in the triangle. One of the properties of the sides of a right triangle is the Pythagorean theorem. The Pythagorean theorem states the following:

`a^2+b^2=c^2`

Where (a) and (b) are the legs of the right triangle, or the sides adjacent to the right angle. (c) is the side opposite the right angle of the triangle triangle, in other words, the hypotenuse. Substitute the respective legs into the formula for the Pythagorean theorem and solve for the unknown,

`a^2+b^2=c^2`

Substitute,

`a^2+b^2=c^2`

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

`80^2+PR^2=89^2\\`

Simplify,

`80^2+PR^2=89^2\\`

`6400+PR^2=7921`

Inverse operations,

`6400+PR^2=7921`

`PR^2=1521\\\\PR=39`

Answer 2

PR = 39 cm

Explanation:

Using Pythagoras' identity in the right triangle

PR² + PQ² = QR² , that is

PR² + 80² = 89²

PR² + 6400 = 7921 ( subtract 6400 from both sides )

PR² = 1521 ( take the square root of both sides )

PR =
`√(1521)` = 39