To find the length of the diagonal of the rectangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Firstly, let's identify the sides of the rectangle. You have two sides of lengths 9 cm and 9√3 cm, which meet at a right angle since rectangles have right angles at each corner.
Now, let's imagine drawing a diagonal across the rectangle. This diagonal cuts the rectangle into two right-angled triangles, each having sides of 9 cm and 9√3 cm and the diagonal as the hypotenuse.
Using the Pythagorean theorem, the formula to calculate the length of the diagonal (d) is:
d² = a² + b²
where 'a' and 'b' are the lengths of the two sides of the right-angled triangle.
In this case:
a = 9 cm
b = 9√3 cm
So:
d² = (9 cm)² + (9√3 cm)²
= 81 cm² + (81 * 3) cm²
= 81 cm² + 243 cm²
= 324 cm²
Now, take the square root of both sides to solve for the length of the diagonal (d):
d = √324 cm²
d = 18 cm
Thus, the length of the diagonal of the rectangle is 18 cm.
