Answer:
a. P = 6x + 6
b. 24 cm by 15 cm
c. 24 cm x 15 cm = 360 cm²
Explanation:
Hmm, it's been an hour and no one's answered yet, but this looks pretty simple.
I'm seeing a rectangle with sides 2x and (x+3), and it asks for the perimeter.
It then tells us right below that that "Perimeter means all the sides added together," and it gives the shortcut of "double the length" and "double the width," and add them together.
You're familiar with that concept of perimeter? If you were given a rectangle of dimensions 1 x 2, do you know to add 1 + 2 + 1 + 2 = 6? That's just going around the actual perimeter and adding together the four numbers you find.
Easier to group the sides in pairs, so do: (2 + 2) + (1 + 1) = 6
But then simplify that to: 2(2) + 2(1) = 6
And that's just the form 2L + 2W they give in the question.
Good with all that? Good, then just do it with the dimensions of the sides as given:
P(erimeter) = 2(2x) + 2(x+3)
Do you see how that worked? If so, then just work it out:
P = 4x + 2x + 6 = 6x + 6 That's the answer to the first part.
Next they say, "Okay, if the perimeter is 78 cm, then what must the dimensions be?"
Well, we have an equation that tells us the relationship between the perimeter and each of the side lengths, and that's:
P = 6x + 6 from before
So now just let P = 78 and solve for x:
78 = 6x + 6
6x = 72
x = 12 cm
But we're not done yet, of course, because now we have to use that known value of x to compute the lengths of the sides.
Look back at the figure:
The long side is 2x, and now we know that x = 12, so the long side is 24 cm.
The short side is x + 3, so that's just 12 + 3 = 15 cm.
And there's your answer: the rectangle is 24 cm by 15 cm
Next they ask for area, and isn't the formula for area just length times width?
L x W = 24 cm x 15 cm = 360 cm² And there, you've proven that the area is 360 cm.