Question

The boy wants to build rectangular beetle cages to study beetle behavior. He wants all the sides on the base of his cages to be at least 10cm. He also wants the base area to equal 576cm. The answered is

Answer 1

32 cm by 18 cm

16 cm by 36 cm,

48 cm by 12 cm

24 cm by 24 cm

Explanation:

The complete question is

A boy wants to build rectangular cages. He wants all the sides on the base of his cages to beat least 10 cm long.he also wants the base area to equal 576 cm2. The boy needs help to find all the possible lengths and widths for the base of the cages. He used only whole centimeters, with no fractional parts.what are all the possible dimensions for the rectangular base?

we know that

The number 576 decompose in prime factors is the same that write

`576=(2^6)(3^2)`

To find out possible side lengths, multiply different combinations of these prime numbers together (make sure each pair adds up to 10)

3x3=9cm 2x2x2x2x2x2= 64cm ----> is not a combination (one side is not greater than 10)

3x3x2= 18cm 2x2x2x2x2= 32cm

3x3x2x2= 36cm 2x2x2x2= 16cm

3x2x2= 12cm 3x2x2x2x2= 48cm

3x2x2x2= 24cm 3x2x2x2= 24cm

therefore

32 cm by 18 cm

16 cm by 36 cm,

48 cm by 12 cm

24 cm by 24 cm