The area of a right triangle is found using the formula 1/2 x base x height.
Using the provided information the equation becomes:
60 = 1/2 * 5x * (3x-1)
Combine 1/2 and 5x:
60 = 5x/2 * (3x-1)
Multiply each term by 2/5:
24 = 3x^2 - x
Subtract 24 from each side:
3x^2 - x - 24 = 0
Now factor the polynomial:
(x-3)(3x+8) = 0
Solve for each x for 0:
3-3 = 0, so x = 3
3x +8 = 0 : subtract 8 from each side:
3x = -8
divide both sides by 3: x = -8/3
Since a side of a triangle cannot be a negative value, we now know x = 3
Now replace x in each side with 3 and solve:
5x = 5(3) = 5 x 3 = 15
3x-1 = 3(3)-1 = 9-1 = 8
