Can you show me how to do this math 0990 problem

[From: ] [author: ] [Date: 11-04-22] [Hit: ]

C is the hypotenuse.)a = 8 metersb = C - 2 meters8² + (c - 2)² = c²64 + (c² - 4c + 4) = c² (FOILed (c-2)²)-4c + 4 + 64 = 0 (Subtracted c² from both sides)-4c + 68 = 0 (Combined like terms)-4c = -68 (Subtracted 68 from both sides)4c = 68 (Divided by negative one to make C positive)c = 17 (Divided by 4)Since C = 17andB = C - 2thereforeB = 17 - 2 = 15-I would start by drawing the triangle out and labeling the shortest side with 8, the longest leg with x and the hypotenuse with x+2. then you can use the pathagorean theorem to get 64+x^2= x^2 + 4x + 4.then Id get all my terms with x to one side and all my constants to the other side by subtractingthe x squared and the 4 from both sides, leaving you with 60=4x.......

The length of the longer leg of a right triangle is two meters less than the length of the hypotenuse. If the shorter leg is 8 meters long, what is the length of the longer leg?

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a² + b² = c² (Pythagorean theorem. A/B are sides. C is the hypotenuse.)

a = 8 meters
b = C - 2 meters

8² + (c - 2)² = c²
64 + (c² - 4c + 4) = c² (FOILed (c-2)²)
-4c + 4 + 64 = 0 (Subtracted c² from both sides)
-4c + 68 = 0 (Combined like terms)
-4c = -68 (Subtracted 68 from both sides)
4c = 68 (Divided by negative one to make C positive)
c = 17 (Divided by 4)

Since C = 17
and
B = C - 2
therefore
B = 17 - 2 = 15

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I would start by drawing the triangle out and labeling the shortest side with "8", the longest leg with "x" and the hypotenuse with "x+2". then you can use the pathagorean theorem to get 64+x^2= x^2 + 4x + 4.
then I'd get all my terms with x to one side and all my constants to the other side by subtracting the x squared and the 4 from both sides, leaving you with 60=4x. Then divide both sides by 4 to get x alone and then x equals 15 :)

Hope this helps!

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Pythagorean Theorem: a^2 + b^2 = c^2
8^2 + x^2 = (x+2)^2
64 + x^2 = (x+2)(x+2) (FOIL)
64 + x^2 = x^2 + 4x +4 (Subtract x^2 from both sides)
64 = 4x + 4
60 = 4x (Subtract 4 from both sides)
15 = x (Divide both sides by 4)
The length of the longer side is 15 meters long.

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Let a be the shorter leg, b be the longer leg, and c be the hypotenuse.
b = c - 2
a = 8

a^2 + b^2 = c^2

8^2 + (c-2)^2 = c^2
64 + c^2 - 4c + 4 = c^2
64 - 4c + 4 = 0
68 - 4c = 0
68 = 4c
c = 17
b = c - 2 = 17 - 2 = 15

So, the length of the longer leg is 15 meters.

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let the length of hypotenuse = h m
then length of longer leg = (h-2)m
given, shorter leg=8 m

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