Question

In the given figure ABCD is a parallelogram. AE is perpendicular on DC and CF is perpendicular on AD. If AB = 10 cm, AE = 8 cm and CF = 12 cm. Find AD.

Answer 1

Hint: For solving this question you should know about the parallelogram and the general properties of a parallelogram. In this problem first we will find the area of a parallelogram by the first side and then we will find this again by the second side. And by comparing both of these we find the value of AD.

Complete step by step solution:
According to the question it is asked to find the value of AD in a parallelogram ABCD and all other given values can be used for determining this.

So, if we look at the diagram then we can say that \[AE\bot DC\] and \[CF\bot AD\] and AB = 10cm, AE = 8cm, CF = 12cm, and now what will be the value of AD = ?
So, \[\Rightarrow \] AB = DC = 10cm (opposite sides of parallelogram are equal)
\[\Rightarrow \] Let’s find the area of parallelogram with height AE and base DC.
\[\Rightarrow \] Area of parallelogram ABCD \[=h\times h\]
\[\Rightarrow \] Area of parallelogram ABCD \[=DC\times AE\]
                                                           \[=10\times 8\]
\[\therefore \] Area of parallelogram ABCD \[=80c{{m}^{2}}-\left( 1 \right)\]
\[\Rightarrow \] Now, to find the area of the parallelogram let CF be the height and AD will be the base.
\[\Rightarrow \] Area of parallelogram ABCD \[=CF\times AD\]
\[\Rightarrow \] \[80=12\times AD\] (from (1))
\[\Rightarrow \] \[AD=\dfrac{80}{12}\]
\[\therefore AD=6.6\] cm.
So, the value of AD is 6.6cm.

Note: While solving the parameters or are of a parallelogram always mind that the height and base can be different – different for a parallelogram but the pair of these will be fix and by that pair the area will be same for a parallelogram and with the help of this property we can find undefined parameters.