Answer:
So first we need to get the perimeter formula. P = 2(w+l). We know P but we dont know w and h.
280/2 = 140. So now we know that 140 = w+l. We also know that the length is 4/3 times greater than the width (we used the ratio). To prove this 3*4/3 = 4, just like in ratio. So we have 2 equations
140 = w+l
l = 4/3w
Now we can plug into 140
140 = w+4/3w
So if you solve algebraicly you get
60 = w.
Now we can find that the length =
80 is the answer to length..
Now to prove answer 60+80 = 140.
So the answer is
The length of the rectangle is 80cm and the width is 60cm
The perimeter of the rectangle is given as 280cm and the ratio of the length to width is 3:4.
The formula of perimeter of rectangle is given as;
[tex]P=2(L+W)[/tex]
This implies that
[tex]280=2(l + w)\\280=2l+2w\\l+w=140...equation(i)[/tex]
But let's go back to our given ratio
3:4 = l:w
3l = 4w
make w the subject of formula
[tex]w = (3/4)l[/tex]
Let's substitute this into equation (i)
[tex]l+w=140\\w=(3/4)l\\l+(3/4)l=140\\(7/4)l=140[/tex]
solve for l
[tex]\frac{7}{4}l=140\\4*140 = 7l\\560=7l\\l= 560/7\\l=80[/tex]
Since L = 80, let's substitute it into equation (i)
[tex]l+w = 140\\80+w = 140\\w = 140 - 80\\w = 60[/tex]
From the calculations above, we have the following data
The length of the rectangle is 80cm and the width is 60cm
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