SOLUTION: If the altitude and base of a parallelogram are increase by 5 inches, the area will increase by 50 sq. inches. If the altitude is increased by 3 inches and the base is decreased b

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: If the altitude and base of a parallelogram are increase by 5 inches, the area will increase by 50 sq. inches. If the altitude is increased by 3 inches and the base is decreased b      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1146434: If the altitude and base of a parallelogram are increase by 5 inches, the area will increase by 50 sq. inches. If the altitude is increased by 3 inches and the base is decreased by 2 inches, the area will increase by 5 sq. inches. Determine the original value of the base of the parallelogram.
a. 3.2 inches ​ ​ ​ ​c. 3.8 inches
b. 4.2 inches ​ ​ ​ ​d. 5.2 inches
Found 2 solutions by richwmiller, KMST:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
a=b*h
a+50=(b+5)*(h+5)
a+5=(b-2)*(h+3)
Three equations with three unknowns plus four possible values for a



Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Ah .
"If the altitude and base of a parallelogram are increased by 5 inches, the area will increase by 50 sq. inches" translates to
%28b%2B5%29%28h%2B5%29=b%2Ah%2B50 .
That simplifies to b%2Ah%2B5b%2B5h%2B25=b%2Ah%2B50 , and
highlight%285b%2B5h=25%29 .
"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
%28b-2%29%28h%2B3%29=b%2Ah%2B5 .
That simplifies to b%2Ah%2B3b-2h-6=b%2Ah%2B5 , and
highlight%283b-2h=11%29 .
Then, it is a question of solving the system of equations
system%285b%2B5h=25%2C3b-2h=11%29 for b and h .