Question

The length of a rectangle is 3 cm more than the width. the area is 70 cm squared. find the dimensions of the rectangle

Answer 1

I am setting the length equal to L and the width equal to L - 3.  We can do this because we know the width is equal to 3 cm less than the length.  Because the area of a rectangle is equal to length times width, we can set up this equation:

L * (L - 3) = 70

Now, we can solve for L.  We start by distributing the L.

$L^{2} -3L=70$

Next, we subtract 70 from both sides.

$L^{2} -3L-70=0$

Now, we can factor this equation.  It becomes:

$(L-10)(L+7)=0$

The zeros of this equation are:

L = 10, -7

Since the rectangle can't have a width of -7, we use positive 7 instead.  So, the dimensions of this rectangle are 10 cm X 7 cm