Question

② a rectangle is 3 meters wide and 10 meters long. how long is the diagonal of the rectangle?

Explanation:

Step1: Recall the Pythagorean theorem

For a rectangle, the diagonal forms a right triangle with the length and width, so we use the Pythagorean theorem \( c = \sqrt{a^2 + b^2} \), where \( a \) and \( b \) are the length and width, and \( c \) is the diagonal. Here, \( a = 10 \) meters and \( b = 3 \) meters.

Step2: Substitute the values into the formula

First, calculate \( a^2 \) and \( b^2 \): \( 10^2 = 100 \) and \( 3^2 = 9 \). Then add them: \( 100 + 9 = 109 \). Finally, take the square root: \( c = \sqrt{109} \approx 10.44 \) meters.

Answer:

The length of the diagonal is approximately \( \boldsymbol{\sqrt{109} \approx 10.44} \) meters (or exactly \( \sqrt{109} \) meters).