In triangle PQR, S is a ponit on PR and QS is the median of the tiangle PQR. If PQ = 3, QR = 5 and PR = 4, then find the length of QS.

In a triangle PQR, QS is the median, and sides PQ = 3, QR = 4, PR = 5.

The median of the triangle is given by

\$QS = \sqrt{\frac{2(QR) ^2 + 2(PQ) ^2 - (PR) ^2}{4}} \$

Substitute the values.

\$\Rightarrow QS = \sqrt{\frac{2(5) ^2 + 2(3) ^2 - (4) ^2}{4}} \$

Calculate the exponents.

\$\Rightarrow QS = \sqrt{\frac{2(25) + 2(9) - 16}{4}} \$

Multiply.

\$\Rightarrow QS = \sqrt{\frac{50 + 18 - 16}{4}} \$

Add and subtract.

\$\Rightarrow QS = \sqrt{\frac{52}{4}} \$

Cancel out common factor.

\$\Rightarrow QS = \sqrt{\frac{\cancel{52} ^{13}}{\cancel{4} ^1}} \$

Answer

The value of the median QS of triangle PQR = \$\sqrt{13}\$.