Question

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if two sides of right angle triangle is consecutive even integers and their area is 24 cm. find hypotenuse of triangle​

Answer 1

Answer:

10 cm

Explanation:

Let a side of the triangle be x.

Other side= (x+2) cm {consecutive even integers differ by 2. U can also take (x-2) cm}

Area = 24 cm^2

1/2 *b*h = 24

x(x+2) = 24*2

x² + 2x = 48

x² + 2x - 48 = 0

x² + 8x - 6x - 48 = 0

x(x+8) - 6(x+8) = 0

(x+8)(x-6) = 0

x=-8 or 6

Thus, x= 6 cm [length can't be -ve]

Sides= x & (x+2) = 6 & 8 cm

Hypotenuse= √(6² + 8²) = √(36 + 64) = √100 = 10 cm

Hope it helps...