This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the circumference of the circle. The diameter of the circle is given as D = 27 cm. The formula for the circumference C of a circle is C = D. C = × 27 cm Using ≈ 3.14159: C ≈ 3.14159 × 27 cm C ≈ 84.823 cm Step 2: Calculate the hypotenuse of the right-angled triangle. The lengths of the two shorter sides (legs) of the right-angled triangle are a = 21 cm and b = 28 cm. Using the Pythagorean theorem, a^2 + b^2 = c^2, where c is the hypotenuse: c^2 = (21 cm)^2 + (28 cm)^2 c^2 = 441 cm^2 + 784 cm^2 c^2 = 1225 cm^2 c = sqrt(1225 cm)^2 c = 35 cm Step 3: Calculate the perimeter of the triangle. The perimeter P_T of the triangle is the sum of its three sides: P_T = 21 cm + 28 cm + 35 cm P_T = 84 cm Step 4: Compare the circumference of the circle and the perimeter of the triangle. Circumference of the circle C ≈ 84.823 cm. Perimeter of the triangle P_T = 84 cm. Since 84.823 cm > 84 cm, the circumference of the circle is greater than the perimeter of the triangle. We have shown that the circumference of the circle (84.823 cm) is greater than the perimeter of the triangle (84 cm). Drop the next question!