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The hypotenuse of a right triangle is 4 meters more than three times the length of the shorter . The length of the longer leg is less than that of the hypotenuse. Find the length of the shorter leg of the triangle .

Sagot :

rywardghimire

Answer:

The hypotenuse of a right triangle is 4m longer than the shorter leg and 2m longer than the longer leg. What are the lengths of the sides?

Just for variety, consider the hypotenuse = h, the short leg h-4 and the long leg h-2.

c^2 = a^2 + b^2; so h^2 = (h-4)^2 + (h-2)^2; h^2 = h^2 - 8h + 16 +h^2 -4h +4;

h^2 -12h +20 = 0 factors to (h - 10)(h - 2) = 0 so h = 2 or h = 10

Since (h - 2) = (2 - 2) = 0 and a triangle cannot have a side of zero length, 10 is the length of the hypotenuse.

h^2 = (h-4)^2 + (h-2); 10^2 = (10-4)^2 + (10-2); (10)^2 = (6)^2 + (8)

The hypotenuse is 10 cm, short leg 6 cm and long leg 8 cm.

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