Question 196134
Start with the formula for the area of a rectangle:
{{{A = L*W}}} and this is equal to 28,700 sq.ft.
Now do the formula for the perimeter of a rectangle:
{{{P = 2(L+W)}}} and this is equal to 960 ft.
Rewrite the perimeter as:
{{{2(L+W) = 960}}} Divide both sides by 2.
{{{L+W = 480}}} Rearrange:
{{{L = 480-W}}} Substitute this for L in the area equation below:
{{{L*W = 28700}}}
{{{(480-W)*W = 28700}}} Simplify.
{{{480W-W^2 = 28700}}} Rearrange:
{{{W^2-480W+28700}}} Factor:
{{{(W-410)(W-70) = 0}}} Apply the zero product rule.
{{{W-410 = 0}}} or {{{W-70 = 0}}} so...
{{{W = 410}}} or {{{W = 70}}} Choose the smaller value for the width, W:
{{{W = 70}}} and...
{{{L = 480-W}}}
{{{L = 480-70}}}
{{{L = 410}}}
The length of the painting is 410 ft.
The width of the painting is 70 ft.