Question

In the diagram PTR and QRS are straight lines. Given that $\tan x^{\circ }=\frac{4}{3}$ and $T$ is the midpoint of $PR$,. Then the length of $PQ$ in cm is

• A. $\sqrt{8}$
• B. $9$
• C. $\sqrt{59}$
• D. $10$

Answer 1

The correct option is D $10$

In triangle $RST\tan x=$$\frac{4}{3}$$=$$\frac{RT}{RS}$

Then $RT=4cm$ and $T$ is the mid point of $PR$

Then $PR=2,RT=$$2\times 4=8$ cm. and $RQ=6cm$ (given )

Then $P{Q}^2=R{Q}^2+P{R}^2=(6{)}^2+(8{)}^2=36+84=100$

Or $PQ=10$ cm