the length and breadth of a rectangle are 10 centimetre and 6cm respectively what is its length of diagonal
Answers
Step-by-step explanation:
This looks like the Pythagorean triple 3, 4, 5. i.e. 3^2 + 4^2 = 5^2, i.e. 9+16 = 25. Except the numbers are doubled (a scaling by a factor of 2) to 6, 8 and 10. i.e. 6^2 + 8^2 = 10^2, that is 36 + 64 = 100. If you draw your rectangle with the diagonal, using Pythagoras Theorem, you will see that one side is 8 cm. . So the sides are 6 cm and 8 cm giving an area of 6x8 = 48 cm^2.
Solution!!
The length and breadth of a rectangle are given in the question. According to the question, we are asked to find the length of the diagonal of the rectangle. So, observing the figure in the attachment, we see that it is forming a right angled triangle, as the corners of the rectangle are at the angle of 90°, we can apply Pythagoras Theorem to calculate the hypotenuse which is the diagonal of the rectangle. The length and breadth of the rectangle are the base and perpendicular of the right angled triangle.
Length = 10 cm
Breadth = 6 cm
(Base)² + (Perpendicular)² = (Hypotenuse)²
(10 cm)² + (6 cm)² = (Hypotenuse)²
100 cm² + 36 cm² = (Hypotenuse)²
136 cm² = (Hypotenuse)²
√136 cm² = Hypotenuse
Hypotenuse ≈ 11.67 cm
Hence, the length of the diagonal of the rectangle is 11.67 cm approximately.
