Answer:
Step-by-step explanation: I always like to make sure I am clear about the question. It seems like the question is:
you have 3 variables; H, N, and S. Using ( ) to represent multiplication
If
(H)(N) = 20cm [H times N is equal to 20 cm]
and
(H)(S) = 6cm [H times S is equal to 6 cm]
then what does
(N)(S) = ? [N times S equals what?]
since H is used in both equations, we know they are the same number, so H has to be a number that is a factor (meaning what are the individual numbers in a multiplication equation)
Since (H)(N) = 20 H represents one of the individual numbers. And the factors of 20 are (1, 2, 4, 5, 10. 20)
Since (H)(S) = 6 H represents one of the individual numbers. And the factors of 6 are (1, 2, 3, 6)
The only number that is the same in each group of factors is 2
So H = 2. Now we can replace H with the number 2
(H)(N)=20 is (2)(N) = 20; Then you divide both sides by 2 and you get
(2)(N)/2 = 20/2 ; the 2 on the left side cancel each other and 20/2 = 10
N =10
You do the same process for (H)(S) = 6
(2)(S) = 6
(2)(S)/2 = 6/2
S = 3
(N)(S) = ?
(10)(3) = 30 cm
so 30 cm is the answer