Question

Fill in the correct entries with respect to the properties asked. AD, BE and CF are perpendicular to the sides BC, CA and AB respectively.

Let 2 s = AB + BC + CA.
Area of $△$ABC = $\frac{1}{2}\times \_\_\_\times AB$
Area of $△$ABC = $\frac{1}{2}\times BC\times \_\_\_$
Area of $△$ABC = $\sqrt{\_\_\_(s-AB)(s-CA)(s-BC)}$

• A. CF, AD, s
• B. CF, AF, s
• C. CF, AP, s
• D. FC, CD, s

Answer 1

The correct option is A

CF, AD, s

Since AD, BE and CF are perpendicular to the sides BC, CA and AB respectively and s = AB + BC + CA, realise that AD, BE and CF are the heights of the $△$ ABC with respect to bases BC, CA and AB respectively.
So, using the formula, Area = $\frac{1}{2}$ $\times$ base $\times$ height, we have,
Area =$\frac{1}{2}$ $\times$ CF $\times$ AB = $\frac{1}{2}$ $\times$ BC $\times$ AD
Also, we know that if 's' is the semi perimeter, Area = $\sqrt{s(s-AB)(s-CA)(s-BC)}$