Question

picture is here for 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?

Answer 1

The width of metal should be approximately 0.5cm

Explanation:

The shape of the frame(both inner and outer) is rectangular in nature.

Area of a rectangle = Length *Breadth

Since the width of the metal is x and the width of the frame will be uniform all the way around, then the length of the outer frame will be (x+8+x)cm and the breadth of the outer frame is (x+10+x)cm. Given the area of the outer frame to be 100cm², substituting this given parameters into the formula we have;

100 = (x+8+x) * (x+10+x)

100 = (2x+8)(2x+10)

100 = 4x²+20x+16x+80

4x²+36x-20 =0

Dividing through by 4 we have;

x²+9x-5 = 0

Using the general formula where a=1, b = 9, c = -5

x = -b±√b²-4ac/2a

x = -9±√9²-4(1)(-5)/2(1)

x = -9±√81+20/2

x = -9±√101/2

x = -9±10.05/2

x = -9+10.05/2 and -9-10.05/2

x = 1.05/2 and -19.05/2

x = 0.525 and -9.525

Choosing the positive width

x = 0.525cm

x ≈ 0.5cm