A certain right angled triangle has its area numerically equal to its perimeter. The length of each side is an even integer. What is the perimeter?

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24 units

36 units

32 units

30 units

answer is A.

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Detailed Solution

We have been given,
The measure of each side of the right triangle is an even integer unit.
We know its perimeter and area are numerically equal.
Let’s start from even integers i.e.,

2, 4, 6, 8, 10, 12, 14

etc. As we know,
Out of them, only

(6, 8, 10)

make Pythagorean triplet.

∵ 8^{2} + 6^{2} = 10^{2}

Also,

8 + 6 + 10 = 24 (Perimeter)

and,

\frac{1}{2} \times 8 \times 6 = 24 (Area)

Thus,
This group of even integers comply with all the given conditions.
Therefore, the perimeter is equal to

24

units.
Hence, option 2 is correct.

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