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The lengths of the sides of a right-angled triangle are consecutive even integers (in cm). What is the product of these integers?

The lengths of the sides of a right-angled triangle are consecutive even integers (in cm). What is the product of these integers? Correct Answer 480

Concept:

In ΔABC, ∠B is 90° so we using the Pythagoras theorem 

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(Hypotenuse)2 = (base)2 + (Perpendicular)2

(AC)2 = (AB)2 + (BC)2

Calculation:

Let sides of right angle triangle as p, p + 2 and p + 4

As in triangle biggest side is hypotenuse 

(p + 4)2 = (p)2 + (p + 2)2

= p2 + 16 + 8p = p2 + p2 + 4p + 4

= p2 - 4p - 12 = 0

= p2 - 6p + 2p - 12 = 0

= (p - 6)(p + 2) = 0

p = - 2 and 6

- 2  is canceled because the side is always positive

p = 6 the n side of right-angle triangle 6, 8 and 10

Product of these integer = 6 × 8 × 10 = 480

∴ The product of these integers is 480.

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