Question

Which expression gives the length of QR in the triangle shown below?

Answer 1

We use the Pythagoras theorem to find the length of QR


`QR^(2) = QS^(2)+ SR^(2)`

`QR^(2)= 25^(2)+ 17^(2)`, square root both sides

`QR= \sqrt{25^(2)+ 17^(2) }`

Answer 2

`\boxed{\boxed{C.\ \overline{QR}=√(17^2+25^2)}}`

Solution-

As given that m∠S = 90°, so triangle QSR is right angle triangle.

Pythagoras Theorem-

It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

i.e
`\text{Hypotenuse}^2=\text{Base}^2+\text{Perpendicular}^2`

i.e
`\text{Hypotenuse}=\sqrt{\text{Base}^2+\text{Perpendicular}^2}`

Putting the values,

`\overline{QR}=\sqrt{\overline{QS}^2+\overline{RS}^2}=√(17^2+25^2)`