Question

If two squares X and Y have each side of 10 m and 20 m respectively, then the side of the square Z whose area is equal to the sum of the areas of square X and square Y is:

• A. \(10\sqrt3\)
• B. \(10\sqrt2\)
• C. \(10\sqrt7\)
• D. \(10\sqrt5\)

Answer 1

The Correct Option is D

To find the side of square Z whose area is equal to the sum of the areas of squares X and Y, we start by calculating the areas of each square. The formula for the area of a square is \( \text{side}^2 \).

• Area of square X: \( 10^2 = 100 \, \text{m}^2 \)
• Area of square Y: \( 20^2 = 400 \, \text{m}^2 \)

Next, add these areas to get the total area for square Z:

\(100 + 400 = 500 \, \text{m}^2\)

Let \( s \) be the side length of square Z. Then:

\( s^2 = 500 \)

To find \( s \), take the square root of both sides:

\( s = \sqrt{500} \)

We simplify \( \sqrt{500} \):

\(\sqrt{500} = \sqrt{100 \times 5} = \sqrt{100} \times \sqrt{5} = 10 \sqrt{5}\)

Thus, the side of square Z is \( 10\sqrt{5} \) m.