e) Calculate the perimeter of a triangle if the lengths of the two night angled sides are 15 cm and 23 cm . 3. The diameter of Simphiwes bicycle wheel is 510 mm . a) Calculate the circumference of the wheel of Simphiwe's bicyde b) What distance will be covered if the wheel rotates 1000 times? (Give the answer in m .)

To calculate the perimeter of a triangle when the lengths of two sides are given, we can use the formula for the perimeter of a triangle: \[ \text{Perimeter} = a + b + c \] where \( a \), \( b \), and \( c \) are the lengths of the three sides of the triangle. Given that the lengths of the two night angled sides are 15 cm and 23 cm, we can calculate the perimeter as follows: \[ \text{Perimeter} = 15 + 23 + c \] To find the length of the third side, we can use the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] Substituting the given values, we have: \[ 15^2 + 23^2 = c^2 \] \[ 225 + 529 = c^2 \] \[ 754 = c^2 \] Taking the square root of both sides: \[ c = \sqrt{754} \] Now, we can calculate the perimeter of the triangle: \[ \text{Perimeter} = 15 + 23 + \sqrt{754} \] Let's calculate the perimeter of the triangle. Calculate the value by following steps: - step0: Calculate: \(15+23+\sqrt{754}\) - step1: Add the numbers: \(38+\sqrt{754}\) The perimeter of the triangle is approximately 65.45906 cm. Now, let's move on to the next part of the problem. We are given that the diameter of Simphiwe's bicycle wheel is 510 mm. To calculate the circumference of the wheel, we can use the formula: \[ \text{Circumference} = \pi \times \text{Diameter} \] Substituting the given diameter: \[ \text{Circumference} = \pi \times 510 \] Let's calculate the circumference of the wheel. Calculate the value by following steps: - step0: Calculate: \(\pi \times 510\) - step1: Reorder the terms: \(510\pi \) The circumference of the wheel is approximately 1602.212253 mm. Finally, to find the distance covered if the wheel rotates 1000 times, we can multiply the circumference by the number of rotations: \[ \text{Distance} = \text{Circumference} \times \text{Number of rotations} \] Substituting the values: \[ \text{Distance} = 1602.212253 \times 1000 \] Let's calculate the distance covered. Calculate the value by following steps: - step0: Calculate: \(1602.212253\times 1000\) - step1: Multiply the numbers: \(1602212.253\) The distance covered if the wheel rotates 1000 times is approximately 1602212.253 mm or 1602.212253 m.