contestada

the length of a rectangle is 3 feet longer than its width. if its width is decreased by 3 feet and its width is increased by 4 feet, its area would be increased by 8 square feet. what is the length of the rrctanglr?

Respuesta :

Let l,w be the length and width of rectangle

Given l = w+3.

Let the area be A= l*w = (w+3)*w

Also given that (l-3)*(w+4) = A+8

                         (w+3-3)*(w+4) = (w+3)*w + 8

                          [tex]w*(w+4) = w^{2} +3w+8[/tex]

                          [tex]w^{2} +4w = w^{2}+3w+8[/tex]

Subtracting [tex]w^{2}[/tex] and 3w on both sides

                           [tex]w^{2}+4w-w^{2}-3w = 8[/tex]

                                           w=8 feet

l= w+3 = 8+3 = 11 feet

Hence length of rectangle = 11 feet.