question_answer

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

A)  15 cm                         

B)  14 cm 

C)  12 cm             

D)         13 cm 

Correct Answer: C

Solution :

For the given triangle, we have a = 28 cm, b = 30 cm, c = 26 cm So, \[s=\frac{a+b+c}{2}=\frac{28+30+26}{2}\] \[s=\frac{a+b+c}{2}=\frac{28+30+26}{2}\] \[=\frac{84}{2}=42\,cm\] Area of the triangle \[=\sqrt{42(42-28)(42-30)(42-26)}\,c{{m}^{2}}\] \[=\sqrt{42\times 14\times 12\times 16}\,c{{m}^{2}}\] \[=\sqrt{112896}\,c{{m}^{2}}=336\,c{{m}^{2}}\] Area of the parallelogram = Area of the triangle \[\therefore \]Area of the parallelogram \[=336\,c{{m}^{2}}\] \[\Rightarrow \]\[base\times height=336\Rightarrow 28\times h=336\] \[\Rightarrow \]\[h=\frac{336}{28}\,cm=12\,cm\] Thus, the height of the parallelogram = 12 cm