VJesus12 wrote: ↑

Fri Sep 04, 2020 6:11 am

A computer manufacturer claims that a perfectly square computer monitor has a diagonal size of 20 inches. However, part of the monitor is made up of a plastic frame surrounding the actual screen. The area of the screen is three times the size of that of the surrounding frame. What is the diagonal of the screen?

A. \(\sqrt{125}\)
B. \(\dfrac{20}3\)
C. \(\dfrac{20}{\sqrt{3}}\)
D. \(\sqrt{150}\)
E. \(\sqrt{300}\)

Answer: E

Solution:

Since the diagonal = side√2, we have:

20 = side√2

20/√2 = side

Multiplying by √2/√2, we have:

10√2 = side

If we let each side of the monitor, not counting the frame = n, then we can create the following equation:

n^2 = 3[(10√2)^2 - n^2]

n^2 = 3[200 - n^2]

n^2 = 600 - 3n^2

4n^2 = 600

n^2 = 150

n = √150

So, the diagonal of the screen is √150 x √2 = √300.

Alternate Solution:

Since the diagonal = side√2, a side of the monitor is 20/√2 = 10√2. Thus, the area of the monitor, including the screen and the surrounding frame, is (10√2)^2 = 200.

If we let A denote the area of the surrounding frame, the area of the screen is 3A and thus, the total area of the monitor is 3A + A = 4A. Since 4A = 200, we find that A = 50 and the area of the screen is 3A = 150. Then, a side of the screen is √150 = 5√6. Finally, the diagonal of the screen is (5√6) x √2 = 5√12 = √300.

Answer: E