question_answer

The adjacent sides of a parallelogram are 4 cm and 9 cm. What is the ratio of its altitudes?

A)  16 : 81                        

B)  9 : 4                

C)  2 : 3                  

D)  3 : 2

Correct Answer: B

Solution :

A diagonal divides a parallelogram into two triangles of equal area. Area \[\Delta ABC=\frac{1}{2}\times BC\times DE\] \[=\frac{1}{2}\times 4\times {{h}_{1}}=2{{h}_{1}}\] Area \[\Delta BAD=\frac{1}{2}\times AB\times DF\] \[=\frac{1}{2}\times 9\times {{h}_{2}}=\frac{9{{h}_{2}}}{2}\] Since \[\Delta \Beta DC\]and \[\Delta \Beta AD\]are equal in area. \[2{{h}_{1}}=\frac{9{{h}_{2}}}{2}\Rightarrow 4{{h}_{1}}=9{{h}_{2}}\]or \[{{h}_{1}}:{{h}_{2}}=9:4\]