the area of a rectangle is 48 sq.cm. if the width is 1/3 of the length, what are dimensions of the rectangle?

Question

if you do come up with an answer, please give me some directions on how you figured it out!

Answer 1

Width = W
Length = L

WL = 48
3W = L

Substitute the second into the first

W(3W) = 48
3W² = 48
W² = 16
W = ± 4

W must be positive so W = 4
3(4) = L

L = 12

Width = 4cm, Length = 12 cm

Answer 2

For these kinds of questions it is usually best to start by assigning a variable to the values you are trying to find. So in this case let:

l= length of rectangle
w= width of rectangle

Now you just have to write algebra equations that say the same thing as the word sentences in the problem.

the area is 48 sq cm, so
L*w=48

width is 1/3 length
w= 1/3 * L

now you have two equations and two unknowns
L*w=48
w=L/3

There are several ways to solve this but the easiest is probably substitution. Since the second equation is already solved for "w" it is easy to put the value of "w" (which is L/3) in place of "w" in the first equation, giving:

L*(L/3)=48

then solving:

L^2/3=48
L^2=144
L=12

since L*w=48, then 12*w=48, and w=4

L=12
w=4

lets check it
4*12 = 48 so the area of the rectangle checks
and 4 is 1/3 of 12 so that checks

voila

good luck
math is power

Answer 3

The width is 4cm and the length is 12cm.
How did I get this answer?
I'm sure you know that you multiply the width and length of a rectangle to find it's area. Since we knew its area, we pick a number(or at least thats what I did). I picked 4 right off the bat. 48 divided by 4 equals 12. If you divide 12 by 4 you will get an answer of 3, thus letting you know that 4 is equal to 1/3 of 12

Answer 4

Formula for the area of a rectangle is: length x breadth (width).

So if your width = a, then your length = 3a

From the above compute as follows:
3a x a = 48 sq cm
3a^2 = 48
a^2 = 16
a = 4
3a = 12

So your rectangle has one side that is 12 cm and another that is 4 cm. I hope this helps

Answer 5

12 and 4

Answer 6

area = length x width = 48 sq cm
Let x be length, then width = x/3
48 = x(x/3) = x^2/3
x^2 = 48*3 = 144
x = +sqr[144] = 12 cm
x/3 = 12/3 = 4 cm

Answer 7

3W=L so A=W*3W=48 so W^2=48/3=16 so W=4 since it is a distance and cannot be negative. since L=3W, L=3*4=12
all units are sq. cm