**Question:**A rectangle has the perimeter of 38 feet and an area of 48 square feet. What are the dimensions of the rectangle?

Can anyone please tell me how to solve the problem and the answer to it?

**Answers:**

It comes down to knowing the (geometric) properties of a rectangle. For this problem it is really nothing fancy except knowing that a rectangle has opposite sides equal, so the lengths and widths we will call them. So this gives you two pairs of sides in other words.

You should also know the basic formulas for finding the perimeter and area of a rectangle If L is the length and w is the width, the perimeter can be defined as 2L + 2w. The area is simply the length times the width or Lw.

So from here, you can set up your equations.

38=2L+2w

48=Lw

For the top one, you can make things easier by factoring out a 2 and dividing 38 by 2 to cancel it out:

19=L+w

So now we have a system of two equations in two variables:

19=L+w

48=Lw

I would try substituting 48/L for W into the top equation:

19=L+48/L

express L as L^2/L and you can add the fractions together easily:

19=(L^2 +48)/L

multiply both sides by L

19L=L^2 + 48

You are going to end up with a quadratic equation here so you need to set it equal to zero:

L^2-19L+48=0 Before messing around with completing the square or the quadratic formula, first see if you can factor into two binomial terms. In this case, you can!!

(L-16)(L-3)=0 so the value of L can either be 16 or 3

So now, if L is either 16 or 3, we can go back and substitute these values into the other equation:

Lw=48 so if L were equal to 3

3w=48

w=16

but if L were equal to 16

16w=48

w=3

So the way I would write my answer is that it is a 16x3 rectangle. If they ask for further clarification, you can say that if the shorter side is 3 than the longer side would have to be 16.

Hope this was helpful.

since perimeter is adding all of the sides together use the following equation:

2x + 2y = 38

and solve for x and y

x + y = 19

try different numbers that will add to get 19 and multiply to get 48. In this case it would be 16 and 3

width = 3

length = 16

L=length h=height x= times

2L + 2h=38

L x h = 48

the multiples or something of 48 is 4 12 and 3 and 16

3(2)+16(2)=38

and 3 x 16 = 48

so the answer is 3 and 16

but the technique is good old guess and check

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