Question 105985
if L = length of triangle
   W = width of triangle
Then the area of the triangle would be:
eq.1){{{A = LW}}}
the length of a rectangle is increased  by 12 and the width is decreased by 8,the area is unchanged:
eq.2){{{A = (L + 12)(W - 8)}}}
The area is also unchanged if the original length is increased by 5 and the original width is decreased by 4:
eq.3){{{A = (L + 5)(W - 4)}}}
Substituting LW for A in eq2:
{{{LW = (L + 12)(W - 8)}}}
{{{LW = LW  - 8L  + 12W - 96}}}
{{{12W - 8L = 96}}}
{{{12W = 96 + 8L}}}
{{{W = 8 + (2/3)L}}}
Substituting LW for A and (8 + (2/3)L) for W in eq3:
{{{L(8 + (2/3)L) = (L + 5)(8 + (2/3)L - 4)}}}
{{{8L + (2/3)L^2 = (L + 5)(4 + (2/3)L)}}}
{{{8L + (2/3)L^2 = 4L + (2/3)L^2 + 20 + (10/3)L}}}
{{{(2/3)L = 20}}}
{{{L = 30}}}
{{{W = 8 + (2/3)L}}}
{{{W = 8 + (2/3)(30)}}}
{{{W = 8 + 20 = 28}}}
Dimensions of the triangle:
length is 30 units
width is 28 units
area is 840 square units