Area of isosceles triangle with 3:2 ratio sides and 32cm perimeter is 32√2 cm².
Isosceles Triangle and its Area
Given:
Perimeter of the triangle = 32 cm
Ratio of equal sides (a) to base (b) = 3:2
1. Identify variable:
Let x be the common factor representing the equal side and base lengths.
2. Set up equations:
Equal sides: a = 3x
Base: b = 2x
Perimeter: 3x + 3x + 2x = 32
Combine like terms: 8x = 32
3. Solve for x:
Divide both sides by 8: x = 4
4. Calculate side lengths:
Equal sides: a = 3x = 3 * 4 = 12 cm
Base: b = 2x = 2 * 4 = 8 cm
5. Find the area:
Area of an isosceles triangle: 1/2 * base * height
Since the height is not given, use the Pythagorean theorem to find it.
a^2 - (b/2)^2 = h^2
12^2 - (8/2)^2 = h^2
144 - 16 = 128
h = √128 = 8√2 cm
Area: 1/2 * 8 * 8√2 = 32√2 cm^2
Therefore, the area of the isosceles triangle is 32√2 square centimeters.
Question:
The perimeter of an isosceles triangle is 32cm. The ratio of the equal side to base is 3:2. Find the area of the triangle.