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.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)   (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)   (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
.
"If the altitude and base of a parallelogram are increased by 5 inches, the area will increase by 50 sq. inches" translates to
.
That simplifies to , and
.
"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
.
That simplifies to , and
.
Then, it is a question of solving the system of equations
for and .
RELATED QUESTIONS

If the altitude and base of a parallelogram are increased by 5 inches, the area will... (answered by richwmiller)
If the altitude and the base of a triangle are each increased by 4 inches the area of the (answered by ewatrrr)
the sides of a square are 10 inches long. if you increase each side by 50% by how many... (answered by ewatrrr)
the sides of square are 10 inches long. if you increase each side by 50% how many square (answered by ewatrrr,lwsshak3)
If the altitude and the base of a triangle are increased by 2 cm the area would increase... (answered by mananth)
base of a triangle is 10 inches more than its altitude. if base is increased by 5 inches... (answered by sachi)
Find the area of a parallelogram if a base and corresponding altitude have the indicated... (answered by chriswen)
A computer keyboard is 11 inches longer than it is wide. If the length were doubled and... (answered by TimothyLamb)
The volume of the cube is a^3 cubic inches . If we increase the edge of the cube by b... (answered by josgarithmetic)