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 m.

Explanation:

A solar collector is 2.0 m long by 1.5 m wide.

If there is a frame of with x m around the collector and makes the exposed area of the collector 2.5 m², then

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

⇒ 4x² - 7x + 0.5 = 0

⇒ 8x² - 14x + 1 = 0

Now, applying the quadratic formula we get,

`x = \frac{-(- 14) \pm \sqrt{(- 14)^(2) - 4(8)(1)}}{2(8)}`

⇒
`x = (14 \pm 12.806)/(16)`

⇒ x = 1.67 m or x = 0.0746 m

But, x can not be more than 1.5 m so, x = 0.0746 m

Hence, the width of the frame is 0.0746 m. (Answer)