A rectangular block is 2 cm wider than it is high and twice as long as it it wide. Let x cm be the height of the block.
Find an expression for the total surface area, A cm2, in term of x.
Let L,W and H be the dimensions of the rectangular block.
Total surface area
A=2(LW+WH+HL)
So if
H=height=x
then
W=x+2, and
L=2W=2(x+2)
Substitute these values of H,W and L into the equation for A and simplify.
on a piece of paper draw a rectangle paddock 20 cm long and 10 cm wide
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on a piece of paper draw a rectangle paddock 20 cm long and 10 cm wide ?
To find the expression for the total surface area of the rectangular block in terms of x, we need to consider all the faces of the block.
Let's denote the height of the block as x cm.
According to the given information, the length of the block is twice its width. Since the block is 2 cm wider than it is high, the width can be represented as (x + 2) cm.
Now, we can find the expression for the surface area of each face of the block:
1) Top and bottom faces: The surface area of each top and bottom face is equal to the length multiplied by the width. Therefore, the area of both top and bottom faces together is:
2 * (x + 2) * x = 2x(x + 2) cm^2
2) Front and back faces: The surface area of each front and back face is equal to the length multiplied by the height. Therefore, the area of both front and back faces together is:
2 * (x + 2) * x = 2x(x + 2) cm^2
3) Side faces: The surface area of each side face is equal to the width multiplied by the height. Since there are two side faces, the total area of both side faces is:
2 * x * x = 2x^2 cm^2
To find the total surface area, we need to sum up the areas of all the faces:
Total Surface Area (A) = 2x(x + 2) + 2x(x + 2) + 2x^2
= 4x(x + 2) + 2x^2
= 4x^2 + 8x + 2x^2
= 6x^2 + 8x cm^2
Thus, the expression for the total surface area (A) in terms of x is 6x^2 + 8x cm^2.