One leg of a right triangle has a length of 7m. The other sides have lengths that are consecutive integers. Find these lengths.
1 answer:
Answer:
24m and 25m.
Step-by-step explanation:
By Pythagoras Theorem:
h^2 = x^2 + 7 ^2 where h is the hypotenuse and x is the other leg.
But x and h are consecutive integers
so h = x + 1 and:
(x + 1)^2 = x^2 + 49
x^2 + 2x + 1 - x^2 = 49
2x + 1 = 49
2x = 48
x = 24
So the 2 lengths are 24 and 25.
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