Algebra 1????

Question

Find the dimensions of a rectangle if the are is 63cm^2 and the perimeter is 32 cm. if x represents the with of the rectangle.

when your solving one of your steps will be:

63=(16-w)w

or

63=(w-16)w

im not sure if its like that but im just asking if the sixteen would be before or after the w????

Answer 1

for the area A = L x W (length x width) = 63

for the circum C = 2L + 2W = 32
solve for W W = (32-2L)/2
W = (16-L)

Substitute W into first equation:
A = 63 = L x (16-L)

Solve for L : L^2 -16L + 63 = 0
(L - 7) (L - 9) = 0
L = 7 or 9

Solve for W: W = (16-L) = (16-7) = 9
& W = (16-L) = (16-9) = 7

L is usually given as the longer side , ergo L= 9 W = 7

Answer 2

P = 2(L + W)
A = LW

they give you both perimeter and area, plug the numbers in

32 = 2(L + W)
63 = LW

solve for a variable, i just choose L
32 = 2(L + W)
16 = L + W
L = 16 - W

plug L in the second eqution
63 = (16 - W)W

63 = 16W - W^2
0 = -W^2 + 16W - 63

use quadratic formula and you'll get W = 7 or 9

L = 16 - W
L = 16 - 7
L = 9

L = 16 - 9
L = 7

the width = 7cm
the length = 9cm

Answer 3

The perimeter is 32 cm, so half the perimeter is 16 cm.
Half the perimeter is two of the sides; one side has length "w", and the other has length 16 - w. That way, they add up to 16 cm.

The area is one side multiplied by the other: 63 = (16 - w ) w

Answer 4

The correct way would be the first one because one of the sides cant be more than 16 or the perimeter would be more than 32.
You would then get 63=16w-w^2
Then w^2-16w+63=0
Then (w-7)(w-9)=0
Then w:w=7,9
The width is 7cm

Answer 5

l*w=63
2l + 2w=32; l+w = 16
63/w +w = 16 ; 63 = (16-w)w
63 +w^2 = 16w

w^2 - 16w +63 = 0
solve the quadratic for w, substitute into original equation for l

Answer 6

Let length = L and breadth = B
LB= 63
2L + 2B = 32
L + B = 16
L = 16 - B
(16 - B).B = 63
16B - B² = 63
B² - 16B + 63 = 0
(B - 9).(B - 7) = 0
B = 9, B = 7
L = 7,L = 9
Dimensions are 7cm by 9cm

Answer 7

before

because you are seperating the perimeter into two sets. one set with one with and length. there fore 32/2 which equal 16. the reason 16 is before w is because you are subtract the with from the one set so it has to be length if you set w as with.