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. 273 ft b. 241 ft c. 341 ft d. 441 ft

Explanation:

Step1: Determine the type of triangle

Since two angles are \(45^{\circ}\) and one angle is \(90^{\circ}\), it is a \(45 - 45-90\) triangle. In a \(45 - 45 - 90\) triangle, the legs are equal, and the hypotenuse \(c=\sqrt{2}a\) (where \(a\) is the length of a leg). Here, the two non - house sides (legs) are \(100\) ft each.

Step2: Calculate the length of the hypotenuse

Using the formula \(c = a\sqrt{2}\) for a \(45 - 45-90\) triangle with \(a = 100\) ft, we get \(c=100\sqrt{2}\approx100\times1.414 = 141.4\) ft.

Step3: Calculate the total fencing length

The total fencing length \(L\) is the sum of the two legs and the hypotenuse minus the \(100\) ft (house portion). \(L=100 + 100+141.4-100\).

$$L=241.4\approx241$$

Answer:

B. 241 ft