Question 105982
If:
L = length
W = width
The sum of the length and the width of a rectangular region is equal to 205 feet:
eqn 1:{{{L + W = 205}}}
the corresponding positive difference is 35 feet:
eqn 2:{{{L - W = 35}}}
We will use the substitution method.
Isolate W:
{{{L + W = 205}}}
{{{W = 205 - L}}}
Substitute (205 - L) in eq. 2:
{{{L - W = 35}}}
{{{L - (205 - L) = 35}}}
{{{L - 205 + L = 35}}}
{{{2L = 240}}}
{{{L = 120 feet}}}
{{{W = 205 - L = 205 - 120 = 85 feet}}}
Area of the rectangular region is:
{{{A = LW = (120)(85) = 10200}}}
The area of the rectangular region is 10200ft^2.