Answer:
Correct option: Fourth one -> 2.2 cm
Step-by-step explanation:
The inside of the frame is 10 cm by 8 cm. To find the whole frame, we need to add two times the width of the metal to each dimension, so the final dimension is 10+2x cm by 8+2x cm.
The area of the frame itself is the area with the bigger dimensions (10+2x and 8+2x) minus the inside area (80 cm2)
If the final area is 100 cm2, we have that:
Area = (10+2x) * (8+2x) - 80
100 = 80 + 36x + 4x2 - 80
4x2 + 36x -100 = 0
x2 + 9x - 25 = 0
Using Bhaskara's formula to solve the quadratic function, we have:
Delta = 81 + 4*25 = 181
sqrt(Delta) = 13.45
x1 = (-9 + 13.45)/2 = 2.225 cm
x2 = (-9 - 13.45)/2 = -11.225 cm (not a valid measurement)
So the width x of the metal is 2.2 cm
Correct option: Fourth one
