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Ainat [17]
3 years ago
5

How to do the problem

Mathematics
1 answer:
ruslelena [56]3 years ago
5 0

Answer:

1.) x = 14.96ft

2.) The shorter leg is 6 meters

Step-by-step explanation:

1.) a^2 + b^2 = c^2

  • a and b = legs of the triangle
  • c = hypotenuse the longest side

15ft^2 + x^2 = (2x +1)^2

  • 225 + x^2 = (2x^2 + 1^2)
  • 225 = 2x^2 + 1 - x^2
  • 225 = x^2 + 1
  • 225 - 1 = x^2 +1 - 1
  • √224 = √x^2
  • x = 14.9662...

2.) Longer leg a = x+2,  shorter leg b = x, Hyp. c= 2x-2

Equation:

  • (x+2)^2 + x^2 = (2x-2)^2

Solve:

  • (x+2)(x+2) + x^2 = (2x-2)(2x-2)
  • x^2 + 4x + 4 + x^2 = 4x^2 - 8x +4
  • 2x^2 + 4x + 4 = 4x^2 - 8x +4
  • 2x^2 + 4x + 4 - 4x^2 +8x - 4 = 4x^2 - 4x^2 - 8x + 8x + 4 - 4
  • -2x^2 + 12x = 0
  • 2x (-x + 6) = 0

Answers:

  • 2x = 0
  • -x + 6 = 0
  • <u>x=0 -or- x=6</u>

<u>Since x cannot equal 0 due to the known length of the triangle needs to be more than 0 the answer for x equals 0.</u>

<u>B=6</u>

Check:

  • A = x + 2: A= 6 +2 = 8
  • B= 6
  • C = 2x -2: C= 2(6) -2 = 10

8^2 + 6^2 = 10^2

  • 64 + 36 = 100
  • 100= 100
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