Question

A carpet measures 7 feet long and has a diagonal measurement of 74 feet. Find the width of the carpet. Write your answer as a number rounded to the nearest tenth

Answer 1

The width of the carpet is approximately 36.5 feet., using the formula
`\(a^2 + b^2 = c^2\),` where
`\(a\) and \(b\)` are the length and width, and \(c\) is the diagonal, we substitute the given values. Squaring the length (7 feet) and the diagonal (74 feet), we can solve for the width.

Explanation:

To find the width of the carpet, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides. In this case, the length and width of the carpet form the two sides, and the diagonal is the hypotenuse.

Therefore, using the formula
`\(a^2 + b^2 = c^2\),` where
`\(a\) and \(b\)` are the length and width, and \(c\) is the diagonal, we substitute the given values. Squaring the length (7 feet) and the diagonal (74 feet), we can solve for the width.

Rearranging the formula to find the width gives us
`\(b = √(c^2 - a^2)\).`Plugging in the values, we get
`\(b = √(74^2 - 7^2)\),`which simplifies to
`\(b = √(5476 - 49)\), resulting in \(b = √(5427)\)`. The square root of 5427 is approximately 73.7 feet. Rounded to the nearest tenth, the width of the carpet is approximately 36.5 feet.