Question

The length of a rectangle is 4 m more than the width. If the area of the rectangle is 77 m2. How many meters long is the width of the rectangle?

Answer 1

Explanation:

length = width + 4

length×width = 77

using the first in the second equation

(width + 4)×width = 77

width² + 4width = 77

now, what square or squaring factors can create this ?

we are looking for (width + a)(width + b).

we know, this is

width² + (a+b)width + ab

so, what a, b can create 4 (the factor in our actual equation) ?

1, 3 and 2, 2, if we are only looking at whole numbers.

and which of the possibilities can we use to turn 77 into a square number ?

81 is only 4 away ...

2+2 = 4.

aha !

so, we can actually say our equation is

width² + 4width + 4 = 77 + 4

and then

(width + 2)² = 81

width + 2 = 9

width = 7 m

length = width + 4 = 7 + 4 = 11 m