Final answer:
To construct the right-angled triangle with sides 5cm and 6cm, draw two perpendicular line segments XY and XZ, and then connect Y to Z. The length of YZ can be calculated using the Pythagorean theorem, resulting in approximately 7.81cm.
Step-by-step explanation:
Constructing a Right-Angled Triangle
To construct a right-angled triangle with sides XY = 5cm and XZ = 6cm, with the right angle at point X, follow these steps:
- Draw a horizontal line segment XY of length 5cm.
- From point X, draw a vertical line segment XZ of length 6cm, ensuring it is perpendicular to XY using a set square or protractor.
- Connect point Y to point Z. The segment YZ will be the hypotenuse of the right-angled triangle XYZ.
By the Pythagorean theorem, we know that in a right-angled triangle, the square of the length of the hypotenuse (side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Therefore, for our triangle XYZ:
YZ2 = XY2 + XZ2
YZ2 = 52 + 62
YZ2 = 25 + 36
YZ2 = 61
YZ = √61 cm ≈ 7.81 cm (Using a calculator to find the square root)
Therefore, the triangle XYZ is a right-angled triangle with sides measuring 5cm, 6cm, and approximately 7.81cm.