What is the area of a rectangle with a width of 6 feet and a diagonal of 10 feet?

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To find the area of a rectangle when you know its width and the length of its diagonal, you can use the Pythagorean theorem. The formula states that for a right triangle formed by the width, length, and diagonal, the square of the diagonal (hypotenuse) equals the sum of the squares of the other two sides. In this case:

Given:

  • Width (W) = 6 feet
  • Diagonal (D) = 10 feet

Using the Pythagorean theorem:

D2 = W2 + L2

Substituting the known values:

D2 = 102 = 100
W2 = 62 = 36

Now we can set up the equation:

100 = 36 + L2

To find L2, we can rearrange the equation:

L2 = 100 - 36 = 64

So, we take the square root of both sides:

L = √64 = 8 feet

Now that we have both dimensions:

  • Width (W) = 6 feet
  • Length (L) = 8 feet

Finally, we can calculate the area (A) of the rectangle:

A = W × L

A = 6 feet × 8 feet = 48 square feet

Therefore, the area of the rectangle is: 48 square feet.

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