9th Class
Mathematics
Heron's Formula
Question Bank
Heron's Formula
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 \[{{h}_{1}}:{{h}_{2}}=9:4\]