Area of parallelogram

Question

The area of a parallelogram is 123 cm² . Had the base been reduced by 4 cm, the area would have been less by 32 cm². Find the original base of the parallelogram.

Answer 1

Area of paralleogram = base x height

 

First Paralleogram:

base=a

height=b

equation: a x b=123

 

Second parallelogram

base =a - 4

height=b (assume height remains the same)

equation: (a - 4) x b= 123-32=91

 

1. ab=123

2. (a-4)b=91. 

solve these two equations simultaneously

 

from equation 1: b=123/a. lets substitute this into equation 2

 

(a-4)(123/a) = 91

123 - 492/a = 91. 

multiply both sides of equation by a.

123a - 492 = 91a

123a - 91a= 492

32a = 492

a=492/32 = 15.375

 

Ans: original base is 15.375 cm