A triangle and a square have the same perimeters. The sides of the triangle are 6cm, 8cm and 10cm.

A triangle and a square have the same perimeters. The sides of the triangle are 6cm, 8cm and 10cm. What is the area of the square?

We find the perimeter of the triangle by the formula:
R tr. = a + b + c = 6 + 8 + 10 = 24 (cm).
According to the condition of the problem:
R tr. = R sq. = 4 * a = 24 (cm).
a = 24/4 = 6 (cm).
The side of the square is known, we find the area by the formula:
S = a² = 6² = 36 (cm²).
Answer: the area of the square is 36 cm².