Question 10206
You can start with the formulas for the perimeter and area of a rectangle:

{{{P = 2(L + W)}}} = 14 You can rewite this as: {{{L = 7 - W}}} and substitute into the equation for the area.
{{{A = L*W}}} = 10

{{{10 = (7-W)*(W)}}}
{{{10 = 7W - W^2}}} Simplify.
{{{W^2 - 7W + 10 = 0}}} Solve by factoring.

{{{W - 2)(W - 5) = 0}}} Apply the zero product principle.

{{{W - 2 = 0}}} or {{{W - 5 = 0}}}

So, W = 2 or W = 5

The length of the rectangle is 5 and its width is 2.