The area of a rectangle is 192 square feet. The ratio of the width to the length is 3:4. Find the length and the width of the rectangle.
2007-03-28 13:03:13 · 9 answers · asked by famousactor143 3 in Science & Mathematics ➔ Mathematics
xy=192 3x=4y x=4/3y
4/3y(y)=192
y=12, x = 16
2007-03-28 13:07:40 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The ratio thing just means that if you divide the width by a certain number and get 3, you can divide the length by that same number and get 4. That means that 3 times some number, let's call it n, is the width of the triangle and 4 times n is the length. So, since the width times the length is the area, or 192,
(3n)(4n) = 192
Solve this for n.
12n^2 = 192
Divide both sides by 12
n^2 = 16
n = 4
So now you know 3n, or 12, is the width, and 4n, or 16, is the height. And 12 * 16 = 192, which is the area you were given!
P.S. Michelle, getting past your obvious intelligence complex, could you maybe find some more sophisticated way to solve this problem than guess-and-check? Maybe use YOUR brain before criticizing that of others?
2007-03-28 13:09:29 · answer #2 · answered by dac2chari 3 · 0⤊ 0⤋
area = l * w
3w = 4l
w = 4/3 l
by substituing this identity:
area = l * 4/3 l
192 * 3/4 = L^2
L = 12 (sub this back into the identity)
W = 4/3 (12) = 16
to test this: Area = W x L
192 = (16 X 12)
2007-03-28 13:09:37 · answer #3 · answered by (+_+) B 4 · 0⤊ 0⤋
let the width be 3x and length 4x
12 x^2 = 192
x^2 = 16
x = 4
so 16 x 12
2007-03-28 13:09:22 · answer #4 · answered by hustolemyname 6 · 0⤊ 0⤋
12 feet x 16feet
2007-03-28 13:07:12 · answer #5 · answered by Barry S 5 · 0⤊ 0⤋
w=16
l=12
2007-03-28 13:12:04 · answer #6 · answered by Anonymous · 0⤊ 0⤋
xy=192
3x=4y
x=4/3y
4/3y(y)=192
y=12, so x = 16
2007-03-28 13:06:51 · answer #7 · answered by leo 6 · 0⤊ 0⤋
2L + 2w = 192?
2007-03-28 13:07:08 · answer #8 · answered by Anonymous · 0⤊ 0⤋
123456789 u can but two - and one + try to get to 100
its really hard
2007-03-28 13:09:47 · answer #9 · answered by 2 4 1 · 0⤊ 0⤋