In the given figure, triangle PQR is a right-angled triangle at Q. If PQ = 35 cm and QS = 28 cm, then what is the value (in cm) of SR?

In the given figure, triangle PQR is a right-angled triangle at Q. If PQ = 35 cm and QS = 28 cm, then what is the value (in cm) of SR?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& PQ\times QR=QS\times PR\\ & 35\times QR=28\times \sqrt{{\left(35\right)}^2+Q{R}^2}\\ & {\left(\frac{5}{4}QR\right)}^2={\left(35\right)}^2+Q{R}^2\\ & \frac{25}{16}Q{R}^2-Q{R}^2=1225\\ & \frac{9}{16}Q{R}^2=1225\\ & Q{R}^2=\frac{1225\times 16}{9}\\ & QR=\frac{35\times 4}{3}\\ & QR=\frac{140}{3}\\ & S{R}^2=Q{R}^2-Q{S}^2\\ & S{R}^2={\left(\frac{140}{3}\right)}^2-{\left(28\right)}^2\\ & S{R}^2=\frac{{14}^2\left({10}^2-9\times 4\right)}{9}\\ & S{R}^2=\frac{{14}^2\times 64}{9}\\ & SR=\frac{14\times 8}{3}\\ & SR=\frac{112}{3}\\ & SR=37.33\text{ cm}\end{array}$$