----------------------------------------------- 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.
The decimal number that is greater is the one with the largest integer part. If they have the same integer part, the first different decimal place is compared.
Now we are going to order the numbers of the exercise,
