Question

janet is fencing a triangular portion of her yard, which has measurements as shown. she needs fencing for the two sides of the yard that do not include the house. she also needs fencing for the third side of the yard, except for the portion taken up by the house. what is the approximate length of fencing she needs? a. 241 ft b. 441 ft c. 273 ft d. 341 ft

Explanation:

Step1: Identify triangle type

It's a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the legs are equal. One leg is 100 ft, so the other non - house side leg is also 100 ft.

Step2: Calculate hypotenuse length

For a 45 - 45 - 90 triangle, the hypotenuse $c$ and leg $a$ are related by $c = a\sqrt{2}$. Here $a = 100$, so $c=100\sqrt{2}\approx100\times1.414 = 141.4$ ft.

Step3: Calculate total fencing length

The total length of fencing is the sum of the two non - house sides and the hypotenuse minus the length of the house. The two non - house sides are 100 ft each, and the hypotenuse is approximately 141.4 ft. The length of the house is 100 ft. So the total length of fencing $L=100 + 100+141.4−100=241.4\approx241$ ft.

Answer:

A. 241 ft