Question

the length and width of a rectangle are (x+4) cm and x cm respectively. A square has the same perimeter as the rectangle. If you add the areas of the rectangle and the square the results is 94 cm^2. solve for x.

Answer 1

what do u mean by adding the areas of the rectangle and the square

Answer 2

hmm what do you think is the perimeter of the RECTANGLE?

keep in mind that, length = x+4 and width = x

Answer 3

hmm.... well.. is not 4... lemme poke a bit

Answer 4

what do u mean by adding the areas of the rectangle and the square

Answer 5

The problem says if you add it you get 94 cm^2

Answer 6

\(\bf \textit{perimeter of the rectangle}=2l+2w=2(x+4)+2(x)\\ \quad \\
2x+8+2x\implies 4x+8 = \textit{perimeter of the square}\)

Answer 7

so now we know that the perimeter of the rectangle, which equals to the perimeter of the square is 4x +8

now recall that a square has 4 EQUAL SIDES, that means, if we divide the perimeter by 4
we should get 1 side by itself

Answer 8

so.... what would you get for 1 side? in terms of "x" that is

Answer 9

\(\bf \cfrac{4x+8 }{4} \implies \square ?\)

Answer 10

3

Answer 11

\(\bf \cfrac{4x+8 }{4} \implies 3?\)

Answer 12

yes?

Answer 13

well... ahemm we dunno what "x" is for one, and the "x" wen MIA in your answer

Answer 14

went MIA == missing in action =)

Answer 15

x=3 ?

Answer 16

is it? well... we really dunno what "x" is, if we did... then we can just plug it in the original equation and use that, but ... we dunno what "x" is

Answer 17

\(\bf \cfrac{4x+8 }{4} \implies \cfrac{4x}{4}+\cfrac{8}{4}\implies \square ?\)

Answer 18

is not a number, just an expression in terms of "x"

Answer 19

this is what u do...

Answer 20

the perimeter is the same as that of the square. that gives us the following eqn;

2(x+4)+2x=4l
where l=length of side of square

Answer 21

and the sum of the squares equals 94 leaves us with a 2nd eqn, which is;

l^2+x(x+4)=94

Answer 22

the perimeter of the rectangle is the same as the one for the square
you use the perimeter of the rectangle, which is the square's

divide it by 4, you get 1 side for the square, all 4 sides are equal in a square

once you have 1 side for the square, side * side is the area of the square, and add that to the rectangle's area, which is (x+4) * x

Answer 23

simplifying the 2 eqns, we are left with the following;
4x-4l=-8
x^2+4x+l^2=94

Answer 24

so it would stay like that?^^

Answer 25

or it has to be solved

Answer 26

making x the subject in the 1st eqn, we are left with
x=-2+l

Answer 27

substitute that into the 2nd eqn and get the ff;
l=7

Answer 28

now that u have l, substitute l=7 into the 1st eqn. u should have the following
4x-4(7)=-8
4x-28=-8
4x=28-8
4x=20
x=5

Answer 29

are u ok with it now

Answer 30

yes so the x is 5

Answer 31

yes

Answer 32

I got it now Thanks !