Eduardocutie71006idn
Answered

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2. One side of a triangle is 2 decimeters more than the other side of and 4 decimeters less than the hypotenuse. Find the lengths of the three sides.​

Sagot :

AnonymousBetaidn

Let x be the hypotenuse

according to the question , one side is 4 less than the hypotenuse

so we will represent it by x-4

the other side was 2 decimeters more than the other one. which we can represent it as

(x-4) + 2

Next is we use pythagorean theorem

which is a^2 + b^2 = c^2 where a and b are sides and c was the hypotenuse

next is apply the pythagorean theorem with the solutions we got above.

(x-4)^2 + (x - 4 + 2)^2 = x^2

(x-4)^2 + (x-2)^2 = x^2

x^2 -8x + 16 + x^2 -4x + 4 = x^2

x^2 -12x + 20 = 0

Factor

(x-10)(x-2)

x= 10

x= 2

Since the one side says that it was "4 less than the hypotenuse" long , we cannot use the 2 as we will get a negative value for it , so we will use 10

hypotenuse = x = 10

Side = x - 4 = 10 - 4 = 6

Side = x - 2 = 10 - 2 = 8

Therefore we got 10,8,6

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