Above are two different models of the same television. If the screen in the model on the left has a 10-cm diagonal, what is the diagonal of the screen in the model on the right?(2 points)Responses cm20 cm60 cm40 30 cm
The diagonal of a rectangle can be calculated using the Pythagorean Theorem:
d = sqrt(a^2 + b^2)
Let's assume the width of the model on the left is 'a' and the height is 'b'. Since the screen is a rectangle, both models have the same aspect ratio. Let's say the width of the model on the right is 2a and the height is 2b.
Given that the diagonal of the screen in the model on the left is 10 cm, we have:
10^2 = a^2 + b^2
100 = a^2 + b^2
Since the aspect ratio is the same for both models, we can say:
d = sqrt((2a)^2 + (2b)^2)
= sqrt(4a^2 + 4b^2)
= sqrt(4(a^2 + b^2))
= sqrt(4 * 100)
= sqrt(400)
= 20 cm
Therefore, the diagonal of the screen in the model on the right is 20 cm.