Question

large rectangle divided into 4 smaller rectangles .the sides of the smaller rectangles are all whole numbers and the area are as follow top 2 are 70 cm² and 30 cm², bottom 2 are 126 cm² and 54 cm². what is the perimeter of the original rectangle ?

Answer 1

The perimeter of the original rectangle is 24 cm.

Step-by-step explanation:

To find the perimeter of the original rectangle, we need to find the lengths of its sides. We know that the top two smaller rectangles have areas of 70 cm² and 30 cm², while the bottom two smaller rectangles have areas of 126 cm² and 54 cm². Let's label the side lengths of the rectangles as a, b, c, and d from left to right and top to bottom.

We can set up the following equations:

a x b = 70

c x d = 70

a x c = 30

b x d = 30

a x d = 126

b x c = 126

c x b = 54

d x a = 54

Simplifying these equations, we can find that a = 6, b = 5, c = 10, and d = 3. Therefore, the perimeter of the original rectangle is 6 + 5 + 10 + 3 = 24 cm.