math problem?

Question

The 2 sides of a parallelogram are in the ration 3:4. A nd its perimeter is 56cm. Find the length of each of its side.

Answer 1

Let a and b be length of the sides and let a
Then we know that P=2*a+2*b and a=(3/4)*b. For simplicity of calculations, we can rewrite the two equations by multiplying them for a constant: 4*a=3*b and 2*P=4*a+4b=3*b+4*b=7*b. Hence b=(2/7)*P=16 cm. It is now straightforward to find a: a=(3/4)*b=12 cm.

I hope I haven't made any error. Not about math, I mean. Im quite good at it. It's just that...Well, I'm italian actually, so English is not my native language but everything seems clear to me. The grammar and everything else should be ok.

Answer 2

First off, let's call one side of the parallelogram 'a', and the other 'b' (any letter works, just keeping it easy). Now, the sides being in a ratio of 3:4 can be said that a / b = 3 / 4 (a to b equals 3 to 4). Next, to find the perimeter, it would be a + a + b + b (the 4 sides added together), which we know to be 56. So, we can set up an equation that a + a + b + b = 56, or 2a+2b=56, or divided everything by 2 to simplify, a+b=28.

Now going back to a/b=3/4, if we times both sides by b, it gives us a = 3b/4. Now we can take that value, and plug into the second equation, to give (3b/4) + b = 28. 1b + 3/4b = (7/4)b. (7/4)b = 28, so multiplying both sides by 4 to cancel out the fraction, gives 7b=112. Next divide both sides by 7 to get b = 16. So that is the first set of sides, 16cm.

To find the other sides, we already know that a + b = 28, so a + 16 = 28. Subtract 16 from both sides, and a = 12cm.

To test the answer, the sides need to be a ratio of 3:4, or 3/4. 12/16 does reduce down to 3/4, so the answers check.

Answer 3

If you're uncomfortable with using algebra to solve such qns, or even haven't learnt algebra in school yet, you may want to try to solve this qns by drawing a model.

You should know that a parallelogram has 2 equal lengths and 2 equal breaths. Hence, If one length of the parallelogram is 4 units long and one breath is 3 units long, the perimeter of the parallelogram is (4+4+3+3 = 14 units) long.

You can then equate 14 units to 56cm (given to you in the qns).

14 units -> 56cm
1 unit -> 56/14 = 4cm

To find the length,
4 units -> 4 x 4cm = 16cm

To find the breath,
3 units -> 3 x 4cm = 12 cm

Answer 4

16 and 12

Answer 5

In scale:
L=3
W=4
P=L+L+W+W
P=3+3+4+4
P=14

In reality: P=56

Set up EQUIVALENT RATIOS:
Ratio 14....3
Reality 56....L
3 X 56 = 14 X L
....168..=.. 14L
..../14........./14
.......12.=...L
Ratio 14....4
Reality 56....W
4 X 56 = 14 X W
....224..=.. 14W
..../14........./14
.......16.=...L

L=12 & W= 16
12+12+16+16=56

Answer 6

Apply it into equations. =)

Let's make one side L (length) and one side W (width).


3L=4W (the ratio)
and
2L+2W=56 (the equation for perimeter)

Make the first equation into:
L=4/3W

and then substitute.

2(4/3W)+2W=56
8/3W+2W=56
14/3W=56
W=12

L=4/3W
L=4/3(12)
L=16

***Two sides are 12 and two sides are 16.***

=)