Question

1. a rectangular garden has a length of 12 meters and a width of 9 meters. a path runs diagonally across the garden. which of the following calculations will give the length of the path? a. (12 + 9)2 b. (122+92) c. (122 - 92) d. (122÷92)

Explanation:

Step1: Identify the right - angled triangle

The length, width of the garden and the diagonal path form a right - angled triangle, where the length and width are the two legs and the path is the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - angled triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\). Here \(a = 12\) and \(b = 9\), so the length of the path \(l=\sqrt{12^{2}+9^{2}}\).

Answer:

None of the options A, B, C, D are correct as written. If option B is supposed to be \(\sqrt{12^{2}+9^{2}}\) (it seems there is a notation error in the original options), then the correct option is B.