Geometry help?

Question:height of rectangle is 7 1/2mm
perimeter is 34 mm
what is the length of the base of the rectangle?

Answers:
The perimeter is 34 mm and the height is 7.5mm

The formula of perimeter of rectangle is P=2l+2w
34=2(7.5)+2(w)
w=length of base

34-15=2w
w=9.5mm
9.5 mm
4.5333333333333333
You need to use the formula for perimeter. Since the perimeter is the length around the outside of the shape you just add up the length of the sides. So P = length + length + width + width = l + l +w + w = 2l +2w. You know what the width is because it is the same as the height and they give you the perimeter. So 34 mm = 2l + 2(7.5 mm) therefore 34mm = 2l + 15 and 34 - 15 = 2l. If you solve this you will get your answer.
The first answer is correct.

If you double the height that is 15mm and the portion of the perimeter involved with the height. The remainder of the perimeter is the length of the two bases. Since a rectangle has equal opposite sides that means that by dividing the remainder by 2 you will arrive at the base.

2h=15mm
perimeter is 34, so 34 - 15 = 19
19 is the combined length of both bases
By dividing 19 by 2 you arrive at the answer 19/2 = 9.5mm

How is that, not only the answer but how to get there.

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