Question

your friend is looking at laptops for college, and is comparing the different screen sizes. use the diagram and formula below to find the height of the laptop screen. round your answer to the tenths place.
d = \sqrt{w^2 + h^2}
diagram of a rectangle with diagonal d=13.3in, width w=11.3, height h
a. h = 7.0 inches
b. h = 9.9 inches
c. h = 12.9 inches
d. h = 10.7 inches

Explanation:

Step1: Rearrange the formula

We have \( d = \sqrt{w^2 + h^2} \). Square both sides to get \( d^2 = w^2 + h^2 \), then rearrange for \( h \): \( h^2 = d^2 - w^2 \), so \( h=\sqrt{d^2 - w^2} \).

Step2: Substitute values

Given \( d = 13.3 \) and \( w = 11.3 \), substitute into the formula: \( h=\sqrt{13.3^2 - 11.3^2} \). Calculate \( 13.3^2 = 176.89 \) and \( 11.3^2 = 127.69 \). Then \( 176.89 - 127.69 = 49.2 \). So \( h=\sqrt{49.2}\approx7.0 \) (rounded to the tenths place). Wait, no, wait: Wait, 13.3 squared is 13.313.3: 1313=169, 130.3=3.9, 0.313=3.9, 0.30.3=0.09, so (13 + 0.3)^2 = 13^2 + 2130.3 + 0.3^2 = 169 + 7.8 + 0.09 = 176.89. 11.3 squared: (11 + 0.3)^2 = 121 + 6.6 + 0.09 = 127.69. Then 176.89 - 127.69 = 49.2. Wait, but \(\sqrt{49.2}\approx7.0\)? Wait, no, that can't be. Wait, maybe I made a mistake. Wait, 13.3 and 11.3: Wait, 13.3^2 is 176.89, 11.3^2 is 127.69. 176.89 - 127.69 = 49.2. \(\sqrt{49.2}\approx7.014\), which is approximately 7.0. But wait, the options have A as 7.0. Wait, but let me check again. Wait, maybe the diagram has different values? Wait, no, the user provided d=13.3, w=11.3. So h = sqrt(13.3² - 11.3²) = sqrt((13.3 - 11.3)(13.3 + 11.3)) [using difference of squares: a² - b² = (a - b)(a + b)] = sqrt(2 24.6) = sqrt(49.2) ≈ 7.01, so approximately 7.0. So the answer should be A.

Wait, but wait, maybe I misread the values. Let me check again. The diagram says d=13.3in, w=11.3. So yes, h = sqrt(13.3² - 11.3²) = sqrt(176.89 - 127.69) = sqrt(49.2) ≈ 7.0. So option A.

Answer:

A. \( h = 7.0 \) inches