Aju starts from his home and walks x meters in north direction. After that he turns right and walks another x meters. He meets his friends and then reaches back home by the shortest possible path. The area enclosed by the path taken by Aju for the whole journey is 50 m². What is x?

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10m

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Solution

The correct option is A
10m

Let his home be at D.

The path taken by him forms an isosceles right angle triangle.

Area of ∆ABC = $\frac{1}{2} \times x \times x$
Therefore, $\frac{1}{2} \times x^{2}$ = 50 (given)
$\Rightarrow x^{2} = 100$
$\Rightarrow x = 10 m$

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Standard VIII Mathematics

Aju starts from his home and walks x meters in north direction. After that he turns right and walks another x meters. He meets his friends and then reaches back home by the shortest possible path. The area enclosed by the path taken by Aju for the whole journey is 50 m2. What is x?

The correct option is A 10m Let his home be at D. The path taken by him forms an isosceles right angle triangle. Area of ∆ABC = 12×x×x Therefore, 12×x2 = 50 (given) ⇒ x2=100 ⇒ x=10 m

Aju starts from his home and walks x meters in north direction. After that he turns right and walks another x meters. He meets his friends and then reaches back home by the shortest possible path. The area enclosed by the path taken by Aju for the whole journey is 50 m². What is x?

The correct option is A
10m

Let his home be at D.

The path taken by him forms an isosceles right angle triangle.

Area of ∆ABC = $\frac{1}{2} \times x \times x$
Therefore, $\frac{1}{2} \times x^{2}$ = 50 (given)
$\Rightarrow x^{2} = 100$
$\Rightarrow x = 10 m$