Question

Two trees $7m$ and $4m$ high stand upright on a ground. If their bases (roots) are $4m$ apart, then the distance between their tops is

• A. $3m$
• B. $5m$
• C. $4m$
• D. $11m$

Answer 1

The correct option is B

$5m$

Explaination for the correct answer:

From the figure, PQ as the tree of height $7m$ and RS as the tree of height $4m$.

And $$\begin{gathered} QE=QP-PE \\ QE=7-4 \\ QP=3cm \end{gathered}$$

So, consider the triangle QRE, from the Pythagorous theorem,

$$\begin{gathered} Q{R}^2=Q{E}^2+E{R}^2 \\ Q{R}^2=3^2+4^2 \\ Q{R}^2=9+16 \\ Q{R}^2=25 \\ QR=\sqrt{25} \\ QR=5 \end{gathered}$$

Therefore, the distance between the top of the two trees is $5m$.

Hence, option B is correct.