Question

A solar collector is 2,0 m long by 1,5 m wide. It is held in place

by a frame of uniform width around its outside edge. If the
exposed collector area is 2,5 m^2, what is the width of the frame ?

Answer 1

The width of the frame is 0.0746 meters

Step-by-step explanation:

We are told that after the frame has been attached to the solar collector, the area that is left exposed is
`2.5m^2` . As we see in the figure, the dimensions of this area are

`(w-2x)` and
`(l-2x)`

where
`x` is the width of the frame.

The product of these dimensions must equal the exposed area:

`(w-2x)(l-2x)=2.5m^2`

Now since
`w=1.5m` and
`l=2m` we have:

`(1.5-2x)(2-2x)=2.5`

we expand this and solve for x using the quadratic formula:

`4x^2-7x+3=2.5`

`4x^2-7x+0.5=0`

we get two solutions:

`x=1.6753`

`x=0.0746`

We take the second solution i.e
`x=0.0746`, because first one gives a width larger than the dimensions of the solar collector which cannot be possible.

Thus the width of the frame is 0.0746 meters.