Question

rectangle ABCD is split into four smaller rectangles. two of the smaller rectangles are shaded. 4:x = 1:2 for rectangle ABCD, work out the ratio shaded area:unshaded area. give your answer in its simplest form

Answer 1

The simplified ratio of the shaded area to the unshaded area for rectangle ABCD split into four smaller rectangles with a 4:1:2 ratio, is x:(4k - 2x), where k represents the width.

Let the length of the rectangle ABCD be 4k and the width be k. The area of ABCD is (4k) * (k) = 4k².

Two smaller rectangles are shaded, with lengths 4k and widths x. Given that the ratio of lengths is 1:2, the length of each shaded rectangle is k, and the area of one shaded rectangle is (k) * (x) = kx.

The unshaded area of ABCD is the area of ABCD minus the area of the shaded rectangles: 4k² - 2kx.

The ratio of shaded area to unshaded area is kx : (4k² - 2kx). To simplify this ratio, factor out a common factor of k:

`\[ (kx)/(k(4k - 2x)) = (x)/(4k - 2x) \]`

So, the simplified ratio of shaded area to unshaded area is x:(4k - 2x).