71. me problem solving the stage manager of a school
play creates a rectangular stage that has whole number
dimensions and an area of 42 square yards. string lights will
outline the stage. what is the least number of yards of string
lights needed to endlose the stage?

Step-by-step explanation:

Sting lights outlining the stage means that they will go around the perimeter, so we will need to find that.  It gives us the area and the fact that the dimensions, length and width, will be whole numbers.

How do you find the area of a rectangle?  you multiply length by width.  So we need to find two numbers that multiply together to make 42.  There re multiple pairs of numbers that do that, but the question is asking for what the least number of yards of string lights, so we need to find the values that make the perimeter the smallest.

Of course the perimeter is adding up all the sides.  Since there are two lengths and two widths we can solve that like this

length + length +  width + width

2* length + 2*width.

Now we just have to check all the options.    What numbers multiply together to make 42?

2 and 21

6 and 7

14 and 3

Now we just have to check which gives the smallest perimeter

2*2 + 2*21 = 4 + 42 = 46

6*2 + 7*2 = 12 + 14 = 36

14*2 + 3*2 = 28 + 6 = 34

So the smallest perimeter is the second one, where one of the measurements is 6 yards and the other measurement is 7 yards.    There's your answer.