Question

a rectangular garden has a length of 20 yards and a width of 42 yards. A diagonal path runs from one end of the garden to the other. How long is the diagonal path?

Answer 1

Hi there!

Since we have a right-angled triangle, we can use the Pythagorean Theorem to find our answer. The Pythagorean Theorem states the following:
${ a}^{2} + {b}^{2} = {c}^{2}$

In this formula a and b represent the legs of the triangle and c represents the length of the hypotenuse.

Let's substitute our data from the question.
${42}^{2} + 20 {}^{2} = c {}^{2}$

Square.
$1764 + 400 = c {}^{2}$

Add.
$2164 = c {}^{2}$

And finally take the root of both sides. We only need to use the positive solution, since the length of the hypotenuse can't be negative.
$c = \sqrt{2164}$

The answer is B.