It's just a triangle's area!

Geometry Level 3

The leg of a right triangle is equal to one-fifth of the sum of the other sides. The triangle has a perimeter of 1. What is it's area ? Round your answer to 3 decimal places.

BONUS: Can you generalize it for this question:

The leg of a right triangle is equal to 1 n \frac{1}{n} of the sum of the other sides. The triangle has a perimeter of k k . What is it's area ?


The answer is 0.033.

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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1 solution

A simple answer: \large \color{#3D99F6} \text{A simple answer:}

Therefore the answer is 0.033 \large \color{#D61F06} \boxed{\text{Therefore the answer is 0.033}}

BONUS part: \large \color{#20A900} \text{BONUS part:}

the expression is given above so I have generalized it → k 2 ( n − 1 ) ( 4 n 2 + 4 n ) \large \color{#EC7300} \text{the expression is given above so I have generalized it} \\ \to \frac{k^2(n-1)}{(4n^2 + 4n)}

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