Final answer:
To find the perimeter of a rectangle with a length of 24cm and a diagonal of 25cm, we can use the Pythagorean theorem to find the width and then calculate the perimeter by adding up all four sides.
This correct answer is none of the above.
Step-by-step explanation:
To find the perimeter of a rectangle, we add up the lengths of all four sides. In this case, the length of the rectangle is given as 24cm. Since the rectangle is right-angled, we can use the Pythagorean theorem to find the width.
The diagonal of the rectangle is given as 25cm, so we can use the formula a² + b² = c², where a, b are the sides of the rectangle and c is the diagonal. Since we know a = 24cm and c = 25cm, we can plug those values into the formula and solve for b.
After finding the value of b, we can calculate the perimeter by adding up all four sides of the rectangle.
Let's calculate:
- Using the Pythagorean theorem: 24² + b² = 25²
- Simplifying the equation: 576 + b² = 625
- Subtracting 576 from both sides: b² = 49
- Taking the square root of both sides: b = 7
- Calculating the perimeter: 2(24 + 7) = 2(31) = 62cm
Therefore, the perimeter of the rectangle is 62cm. None of the answer choices (a. 68 cm, b. 70 cm, c. 72 cm, d. 74 cm) are correct.
This correct answer is none of the above.