Question

A square of area 36cm is cut to make two rectangles a and b the ratio of area a to b is 2:1 work ou the dimensions of rectangles a and b

Answer 1

The dimensions of rectangle a are 6x4 and dimensions of rectangle b are 6x2.

Explanation:

We are given a square with area 36 squared cm. Therefore, dimension of the square will be 6 cm.

The square is cut into two rectangles with areas in the ratio 2:1.

Let the dimensions of the rectangles be 6*a and 6*b. Therefore, we can set up the ratio of areas as:

`(6a)/(6b)=(2)/(1)  \\a=2b`

Moreover, we can set the combined area of rectangles equal to the area of square to form another equation:

`6a+6b=36\\a+b=6`

Using substitution method, we can solve for 'a' and 'b' as shown below:

`2b+b=6\\3b=6\\b=2`

And

`a=2b\\a=2(2)\\a=4`

Therefore, dimensions of the two rectangles are 6x4 and 6x2, respectively.