Help pls :(

Question

One half area of a rectangular is 54 m^2 . If the triple of the width exeeds twice the length by 3 meter , find the perimeter ?

Answer 1

Let L be the length of the rectangle and W be its width.

 

Then its area A = L * W.  If half the area is 54 m², then the whole area is 108 m²

 

"the triple of the width exeeds twice the length by 3 meter" can be represented as follows"

       3       *      W         =       2   *       L        +   3

 

From this, 3W = 2L + 3 means L = (3W - 3)/2 = 3(W - 1)/2

 

Substituting this value into the formula for area results in the following:

 

L * W = 3(W - 1)/2 * W = 108

 

W ( W - 1) = (2/3) * 108 = 72

W² - W - 72 = 0

(W + 8) * (W - 9) = 0

 

From this W = -8 or 9. Since W must be positive, it cannot be -8.

Then the width W = 9 m and L = 3(W - 1)/2 = 12 m.

 

From this the perimeter of the rectangle is 2(L + W) = 42 m.