----------------------------------------------- Define x: ----------------------------------------------- Let one of the leg be x and the other leg is x + 4.
----------------------------------------------- Formula: ----------------------------------------------- Area of triangle = 1/2 x base x height
----------------------------------------------- Subtract 32 from both sides: ----------------------------------------------- x² + 4x - 32 = 0
----------------------------------------------- Factorise: ----------------------------------------------- (x - 4)(x + 8) = 0 x = 4 or x = -8 (rejected, length cannot be negative)
----------------------------------------------- Find the length of the legs: ----------------------------------------------- One leg = x = 4 miles The other leg = x + 4 = 4 + 4 = 8 miles
-------------------------------------------------------------------- Answer: The 2 legs are 4 miles and 8 miles. --------------------------------------------------------------------
First, define the area of a triangle: A = 1/2bh. Let A = 16, and since it’s a right triangle, the base and the height can easily be translated to its two legs. Let one leg = x, and the other = x + 4. So this would give you the equation: 16 = .5(x)(x+4). Distribute so 16 = .5x^2 + 2x. You might want to get rid of the decimal/fraction, so multiply everything by 2 and this would give you 32 = x^2 + 4x. Recognizing that this will be a quadratic equation let x = 0 and bring everything unto one side, so 0 = x^2 + 4x - 32. Factor. 0 = (x+8)(x-4). Since a leg cannot be negative, x can only equal 4. This means that one leg is 4 and the other is 8.
