Question

The perimeter of a rectangular campsite is 64 cm and its area is 207 cm. Find the length and the breadth of the rectangle.

Answer 1

Answer: w = 9 cm,   L = 23 cm

Step-by-step explanation:

P (Perimeter)  = 2L(length) + 2w(width)

A (Area) = L (length) x w (width)

Use the formulas above to create a system of equations, then solve using the substitution method.

P = 2L + 2w

64 = 2L + 2w

32 = L + w

32 - w = L    ←←←   use this to substitute for L in the Area equation

                              A = L · w

                          207 = (32 - w)w

                          207 = 32w - w²

      w² - 32w + 207 = 0

         (w - 23)(w - 9) = 0

     w - 23 = 0            w - 9 = 0

           w₁ = 23                w₂ = 9

Now, solve for L:

      L₁ = 32 - w₁                      L₂ = 32 - w₂

         = 32 - 23                           = 32 - 9

          = 9                                    = 23

We have 2 sets of solutions (w₁ , L₁) and (w₂ , L₂)

                                              (23, 9)  and  (9, 23)

Notice that they are the same values but in reverse order.  These are the dimensions of the rectangle.  We generally consider width (w) to have the smaller value. So, w = 9 and L = 23

 

Answer 2

Perimeter Formula:
$2l + 2b = 64$


Area Formula:
$l \times b = 207$
Set perimeter Formula equal to b:
$2l + 2b = 64 \\ 2(l + b) = 64 \\ l+ b = 32 \\ b = 32 - l$
Plug formula for be we just made above into the area Formula:
$(32 - l) \times l = 207$


Solve for L (you'll have to use quadratic formula) then plug that back into the area Equation and solve for b.

Here's a link to where the problem has been explained before (they go into more detail than me).

https://brainly.ph/question/468631

lmk if you need any more help