Question

If one side of a right-angled triangle
(with all sides integers) is 15 cm, then
what is the maximum perimeter of the
-triangle?​

Answer 1

The answer is 40 cm.

Explanation:

Given is a right-angled triangle, hence it will follow the Pythagoras formula:

$(side 1)^{2} + (side 2)^{2} = (side 3)^{2}$

Given, the length of one side is 15 cm,

All pythagorean triples are unique.

So,  when one side of the right-angled triangle is 15 cm, the others will be 8 cm and 17 cm respectively.

Therefore, the maximum Perimeter of the right-angled triangle will be,

$= 15 cm + 8 cm + 17 cm = 40 cm.$

Answer 2

The maximum perimeter of the  triangle is 40 cm.

Explanation:

It is given that, one side of a right-angled triangle is 15 cm. For a right angled triangle, one of the angle is 90 degrees and it follows Pythagorean triplet. It means that one of the side is 15 cm and other two sides are 8 cm and 17 cm. It would mean that,

$\sqrt{15^{2}+8^{2}}=17$

Perimeter is the sum of all sides. So,

P = 17 + 8 + 15 = 40 cm

So, the maximum perimeter of the  triangle is 40 cm.

Learn more,

Right angled triangle

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