reese needs a new bike mirror. her old mirror was a rectangle with a length of 10 cm and a width of 5 cm…

Explanation:

Step1: Calculate old mirror area

Area of rectangle: $A_{rect} = l \times w = 10 \times 5 = 50$ cm²

Step2: Calculate area of first circle

Area of circle: $A_{circle} = \pi r^2$. For $r=4$ cm: $A_1 = \pi \times 4^2 = 16\pi \approx 50.27$ cm²

Step3: Calculate area of second circle

For $r=7$ cm: $A_2 = \pi \times 7^2 = 49\pi \approx 153.94$ cm²

Step4: Calculate area of third circle

For $r=8$ cm: $A_3 = \pi \times 8^2 = 64\pi \approx 201.06$ cm²

Step5: Compare to target area

Find area closest to 50 cm².

Answer:

The circular bike mirror with a radius of 4 cm (the first option)