A square has an area of S^2 and a regular hexagon has a perimeter of T. If p is the perimeter of the square and h is a side of the hexagon, then find h+p in terms of S and T.
SQUARE: A=S^2=S.S, Perimeter=P=4S.
REGULAR HEXAGON: Perimeter=T=6h,h=T/6.
h+P=T/6+4S.
square A=S^2, P=p (side of the square must be S, p=4(S))
Regular Hexagon P=T and side=h (side is total perimeter divided by the sides of the hexagon (6))
therefore, h+p in terms of S and T.
(P/6)+ 4S
To find h+p in terms of S and T, we need to determine the expressions for h and p.
Let's start with the square. The area of a square is given by A = side^2. We know that the area of the square is S^2, so we can write:
S^2 = side^2
Taking the square root of both sides, we get:
side = √(S^2)
Since all sides of a square are equal, the perimeter of the square (p) is 4 times the length of a side:
p = 4 * side
= 4 * √(S^2)
= 4S
Now let's move on to the regular hexagon. The perimeter of a regular hexagon is given by the formula P = 6 * side. We know that the perimeter of the hexagon is T, so we can write:
T = 6 * side
Dividing both sides by 6, we get:
side = T/6
So, the length of a side of the hexagon (h) is T/6.
Finally, we can find h+p:
h + p = (T/6) + (4S)
= T/6 + 4S
Therefore, h+p is equal to T/6 + 4S in terms of S and T.
To find the value of h + p in terms of S and T, we need to relate the side length of the hexagon h to the side length of the square S and the perimeter of the square p to the perimeter of the hexagon T.
Let's start by calculating the perimeter of the square p. Since a square has four equal sides, each side length of the square is equal to √S (the square root of S). Thus, the perimeter of the square p is given by:
p = 4 * √S
Next, we can determine the relation between the side length of the hexagon h and the perimeter of the hexagon T. A regular hexagon has six equal sides, so each side length of the hexagon is equal to T/6. Therefore, h = T/6.
Now, we can substitute the values of p and h into the expression h + p:
h + p = (T/6) + 4 * √S
So, h + p, in terms of S and T, is equal to (T/6) + 4 * √S.