Cai went to the store to buy a new TV. The sales clerk asked "How large is your current TV?". Cai replied "It is 39 inches wide and 22 inches tall". The sales clerk explained that TVs are sold by the measurement along the diagonal of the screen. Save Cai a trip home to remeasure - What is the diagonal measurement for Cai's current TV? Round your answer to the nearest whole number. Cai has a

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To find the diagonal measurement of Cai's current TV, we can use the Pythagorean theorem. The formula is:

$$
d = \sqrt{w^2 + h^2}
$$

where $$d$$ is the diagonal, $$w$$ is the width, and $$h$$ is the height.

Given:
- Width ($$w$$) = 39 inches
- Height ($$h$$) = 22 inches

Now, we can plug in the values:

$$
d = \sqrt{39^2 + 22^2}
$$

Calculating $$39^2$$ and $$22^2$$:

$$
39^2 = 1521
$$
$$
22^2 = 484
$$

Now, add these two results:

$$
d = \sqrt{1521 + 484} = \sqrt{2005}
$$

Now, we calculate $$\sqrt{2005}$$:

$$
\sqrt{2005} \approx 44.83
$$

Rounding to the nearest whole number, the diagonal measurement for Cai's current TV is approximately:

$$
\boxed{45} \text{ inches}
$$
The diagonal measurement of Cai's TV is approximately 45 inches.

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