In an isosceles triangle with an area of 48 cm2, the length of the side to the length of the base is 5 to 8. Find the length of the side.

| January 4, 2021 | education

An isosceles triangle is a triangle whose sides at the base are equal. To calculate the area of ​​a triangle, we use Heron’s formula: S = 1/4 * b * √ (4 * a ^ 2 – b ^ 2), where S is the area of ​​the triangle, a is the side of the triangle, b is the base of the triangle.
Let’s take for x (cm) – the length of the sides of the triangle, then (8 * x) (cm) – the length of the base and (5 * x) – the length of one side.
Substitute the values ​​S = 48 (cm2), a = (5 * x) and b = (8 * x) into the formula:
48 = 1/4 * (8 * x) * √ (4 * (5 * x) ^ 2 – (8 * x) ^ 2).
48 = 2 * x * √ (4 * 25 * x ^ 2 – 64 * x ^ 2).
48 = 2 * x * √ (100 * x ^ 2 – 64 * x ^ 2).
48 = 2 * x * √ (36 * x ^ 2).
48 = 2 * x * 6 * x.
48 = 12 * x ^ 2.
x ^ 2 = 48/12 = 4.
x = √4 = 2 (cm).
Means: 2 (cm) * 5 = 10 (cm).
Answer: the side length is 10 centimeters.



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