Question

Alex starts from his home and walks $x$meters north. He then turns right and walks another $x$ meters. He meets his friends and returns home using the shortest path possible. The area enclosed by the path taken by Alex for the whole journey is $50$ square meters. Find the value of $x$.

• A. $6m$
• B. $7m$
• C. $\sqrt{50}$
• D. $10m$

Answer 1

The correct option is D $10m$

Let’s draw the path Alex took for his journey. Let the position of his home be D.

The path taken by him forms an isosceles right triangle.

Area enclosed by the path taken by Alex $=50sqm$
Area of $△ABD=\frac{1}{2}\times base\times height=\frac{1}{2}\times x\times x$
$\Rightarrow 50=\frac{1}{2}{x}^2$
$\Rightarrow x^2=50\times 2$
$\Rightarrow x^2=100$
$\Rightarrow x=\sqrt{100}$
$\Rightarrow x=10m$
Hence, the value of $x$ is $10m.$