Question

How to do the problem

Answer 1

1.) x = 14.96ft

2.) The shorter leg is 6 meters

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
• x=0 -or- x=6

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.

B=6

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