Geometry problem?

Question

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In the diagram, the dimensions of a piece of carpeting have been marked in terms of x. All lines meet at right angles. Express the area and the perimeter of the carpeting in terms of x.

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Answer 1

First you need to get the dimensions of the figure. From inspection you can see that the long side is (x+3)+(x+4)=(2x+7) and the short side is (x+2)
And the cutout piece is 2 by (x+3)
So the area of the figure would be the product of the outer dimensions minus the area of the cutout piece.
(2x+7)(x+2) -2(x+3)
Multiply this out and simplify ...
2x^2 + 4x + 7x + 14 - 2x - 6 =
2x^2 + 9x + 8

For the perimenter you need the sum of the edges. Going all around that would be
x + (x+3) + 2 + (x+4) + (x+2) + [(x+3)+(x+4)]
Simplify ...
6x + 18

If different people give you different answers, work this out yourself as described and you'll get it and know it.

Answer 2

P = x + (x + 3) + 2 + (x + 4) + (x + 2) + (x + (x + 4)) = x + x + 3 + 2 + x + 4 + x + 2 + x + x + 4 = 6x + 15

A = x(x + 3) + ((x + 2)(x + 4)) = x^2 + 3x + (x^2 + 4x + 2x + 8) = x^2 + 3x + (x^2 + 6x + 8) = x^2 + 3x + x^2 + 6x + 8 = 2x^2 + 9x + 8

Perimeter = 6x + 15
Area = 2x^2 + 9x + 8

It helps if you draw them as 2 different rectangles. Whereas the length of the right side would be the width of the left rectangle plus the 2 which make up the rigth side.

Answer 3

The perimeter is found by adding the lengths of each side.So p = x+x+3 +2 + x+4 +2+x +2x+7 = 6x + 18.

The area is (x+3)x +(x+4)(x+2)
= x^2+3x +x^2 +6x +8 = 2x^2 +9x +8

Answer 4

you just got to divise your figure in 2 parts and do the area formula for each of them.

you can see than in your figure you have 2 rectangles, the first have a side of (x+4) and a side of (x+2), the second have sides of x and (x+3).

now do the area forula for first: (x+4)*(x+2)= x^2 + 4x + 2x + 8 and for second: (x)*(x+3)= x^2 + 3x

and now add the both together: x^2 + 4x + 2x + 8 + x^2 + 3x = 2x^2 + 9x + 8 so here's your answer!

And for the perimeter it's even easier, you just additionate all the sides witch are :
(x+4), (2),(x+3),(x),(x+4+x+3) and (x+2)

good luck!

Answer 5

The area is...
(2x+7) * (x+2) - 2(x+3)
=2x^2 + 7x +4x +14 -2x -6
=2x^2+9x+8

Perimeter is...
x+(x+3)+2+(x+4)+(2+x)
+(x+4)+(x+3)=6x+18

Answer 6

OK, if we draw a horizontal line dividing the top from the bottom, the top, narrower block is 2*(x+4) or 2x+8

The bottom is (x+3)+(x+4) by x, or x*(2x+7) or 2x^2 + 7x


Adding all terms, we have
2x^2 + 9x + 8

Answer 7

okay well first you have to draw an invisible line to make two quadrilaterals , then you have to use the given terms and plug them into the formulas of Area and Perimeter....then once you have done that for each quadrilateral SEPERATELY, you add them at the end...and you get the answer.....im a sophomore now...so....ya ....hope that helps.....=D