Question

Five rectangles are arranged from the least to the greatest area and named A, B, C, D, and E in order of increasing area. All dimensions are whole numbers, and no 2 rectangles have the same area. Determine the dimensions of all 5 rectangles using the following clues:
The median area is 15 square units.

Rectangles B and D are squares.

Rectangles C and D have the same perimeter.

Rectangles A, B, and C have the same length.

Rectangles D and E have the same length.

Rectangles C and E have the same width.

Answer 1

Given that median area is 15 square units.

Hence rectangle C in the middle has 15 square units.

Its dimensions can be width= 5 and length = 3

SInce B is smaller than C and has the same length, B has lengh of 3 with area = 9 sq units.

D has the same perimeter = 16 units.  Since D is a square, side of D = 4 units.

Now D and E have the same length.  Hence length of E = 4 units.

Width of E = width of C = 5 units.Thus makes the area of E as 20 sq units.

Rectangle A has length =3 and width can be less than 3 since area is smaller than B.

so A has length= 3 width = 2 with area = 6 sq units.