Question

A framing company is putting out a new product this summer. The width of the frame will be uniform all the way around. The designed frame will be cut out of a piece of steel, and to keep the weight down, the final area of the frame alone should be 100 cm2. The inside of the frame has to be 10 cm by 8 cm. What should the width x of the metal be?

11.2 cm

7.4 cm

3.4 cm

2.2 cm

Answer 1

Correct option: Fourth one -> 2.2 cm

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