Final answer:
Using the Pythagorean theorem with a television diagonal of 63cm and a height of 39cm, the width is calculated. After squaring and subtracting the height from the diagonal's square, the square root of the result gives the width, which when rounded is 49 cm.
Step-by-step explanation:
To calculate the width of a television screen with a known diagonal and height, we can apply the Pythagorean theorem since the screen can be considered as having a right-angle triangle shape when looking at its height, width, and diagonal.
The Pythagorean theorem is a fundamental principle in geometry that states that in a right 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. This can be written as c² = a² + b², where c is the hypotenuse, and a and b are the other two sides.
Given that the hypotenuse (diagonal of the screen) is 63cm and the height (one of the sides) is 39cm, we can substitute into the formula to find the width (the other side).
First, square the length of the diagonal: 63² = 3969 cm².
Then, square the height of the screen: 39² = 1521 cm².
Now subtract the square of the height from the square of the diagonal to find the square of the width: 3969 cm² - 1521 cm² = 2448 cm².
Finally, take the square root of 2448 cm² to find the width: √2448 cm² ≈ 49.48 cm. When rounding to the nearest centimetre, the width is approximately 49 cm.