Final answer:
To find the perimeter of an isosceles triangle, use the formula for the area of a triangle to find the height, then calculate the base and the other two sides of the triangle. The perimeter of the triangle is 28 cm.
Step-by-step explanation:
To find the perimeter of an isosceles triangle, we need to know the lengths of its sides. Let's denote the altitude and the base of the triangle as 'h' and 'b', respectively. According to the problem, the base is 4 cm longer than the altitude, so the base can be expressed as 'h + 4'. We also know that the base is the longest side of the triangle. Given that the area of the triangle is 48 cm², we can use the formula for the area of a triangle to find the height: Area = 1/2 × base × height 48 cm² = 1/2 × (h + 4) × h. Now, we can solve this equation to find the height of the triangle. Once we have the height, we can calculate the base and the other two sides of the triangle. Finally, we can add up the lengths of all three sides to find the perimeter of the triangle. The correct answer choice for the perimeter is B. 28 cm.