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

32 cm by 18 cm

16 cm by 36 cm,

48 cm by 12 cm

24 cm by 24 cm

Step-by-step 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

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

they can both be solutions depends on the equation

step-by-step explanation:

what is the equation? ?

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b