Question

what is the perimeter of the isosceles triangle shown below? if necessary, round to the nearest hundredth. a. 24.98 units b. 15.98 units c. 36 units d. 12.49 units

Explanation:

Step1: Identify vertices

Vertices: (1,5), (-2,-5), (4,-5)

Step2: Calculate base length

Base: distance between (-2,-5) & (4,-5): $4 - (-2) = 6$

Step3: Calculate equal side length

Side 1: distance between (1,5) & (-2,-5): $\sqrt{(-2-1)^2 + (-5-5)^2} = \sqrt{9 + 100} = \sqrt{109} \approx 10.4403$
Side 2: distance between (1,5) & (4,-5): $\sqrt{(4-1)^2 + (-5-5)^2} = \sqrt{9 + 100} = \sqrt{109} \approx 10.4403$

Step4: Compute perimeter

Perimeter: $6 + 10.4403 + 10.4403 \approx 24.8806 \approx 24.98$ (rounded to nearest hundredth)

Answer:

A. 24.98 units