Q:

# The diagonal of a right triangle is 10 cm and one side is 8 cm. What is the perimeter of this rectangle

Accepted Solution

A:
I believe there might be a misunderstanding in your question. You mentioned a "rectangle" in your last sentence, but initially, you were referring to a "right triangle." Rectangles have four sides, while right triangles have three sides. If we assume you meant to ask for the perimeter of the right triangle, we can solve it using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side, which is the diagonal in this case) is equal to the sum of the squares of the other two sides. Let's denote the two legs of the right triangle as a and b, and the hypotenuse as c. According to the information you provided, one side (a leg) is 8 cm, and the hypotenuse (the diagonal) is 10 cm. We can use the Pythagorean theorem to find the length of the other leg (b). Using the Pythagorean theorem: a^2 + b^2 = c^2 Since a = 8 cm and c = 10 cm: 8^2 + b^2 = 10^2 64 + b^2 = 100 Now, subtract 64 from both sides: b^2 = 100 - 64 b^2 = 36 Taking the square root of both sides: b = β36 b = 6 So, the other leg (b) of the right triangle is 6 cm. Now that we know the lengths of all three sides, we can calculate the perimeter of the right triangle by adding up the lengths of the sides: Perimeter = a + b + c Perimeter = 8 cm + 6 cm + 10 cm Perimeter = 24 cm Therefore, the perimeter of the right triangle is 24 cm.