Question 1146434
If we call our variables
h=altitude of the parallelogram (in inches), and
b=base of the parallelogram (in inches),
the original parallelogram area (in square inches), is
{{{b*h}}} .
"If the altitude and base of a parallelogram are increased by 5 inches, the area will increase by 50 sq. inches" translates to
{{{(b+5)(h+5)=b*h+50}}} .
That simplifies to {{{b*h+5b+5h+25=b*h+50}}} , and
{{{highlight(5b+5h=25)}}} .
"If the altitude is increased by 3 inches and the base is decreased by 2 inches, the area will increase by 5 sq. inches" translates to
{{{(b-2)(h+3)=b*h+5}}} .
That simplifies to {{{b*h+3b-2h-6=b*h+5}}} , and
{{{highlight(3b-2h=11)}}} .
Then, it is a question of solving the system of equations
{{{system(5b+5h=25,3b-2h=11)}}} for {{{b}}} and {{{h}}} .