Final answer:
To find the perimeter of a right-angled triangle with known side lengths and area, we can use the formula for the area of a triangle. Using this formula, we can solve for the value of x, which represents the lengths of the sides. Once we know the side lengths, we can calculate the perimeter of the triangle.
Step-by-step explanation:
To find the perimeter of a right-angled triangle, we need to sum up the lengths of all three sides. In this case, the two shorter sides are given as 5x cm and 3x-1 cm, and we need to find the value of x to determine their actual lengths. The area of the triangle is given as 60 cm², so we can use the formula for the area of a triangle to find x:
Area = 1/2 * base * height
Plugging in the values, we get:
60 = 1/2 * (5x) * (3x-1)
Simplifying the equation:
60 = 15x² - 5x
15x² - 5x - 60 = 0
Now we can solve this quadratic equation either by factoring or by using the quadratic formula. Once we find the value of x, we can substitute it back into the expressions for the sides to find their lengths. Finally, we can add up all three side lengths to find the perimeter of the triangle.