# Ex.11.2 Q6 Perimeter and Area - NCERT Maths Class 7

## Question

\(DL\) and \(BM\) are the heights on sides \(AB\) and \(AD\) respectively of parallelogram \(ABCD\) (See the below figure). If the area of the parallelogram is \(1470 \,\rm cm^2\), \(AB\)\(= 35 \,\rm cm\) and \(AD\) = 49 cm, find the length of \(BM\) and \(DL\).

## Text Solution

**What is known?**

The area of the parallelogram and its two sides, \(AB\) and \(AD\). \(DL\) and \(BM\) are the heights on sides \(AB\) and \(AD\) respectively of parallelogram \(ABCD\).

**What is unknown?**

The length of the perpendiculars \(DL\) and \(BM\) to sides \(AB\) and \(AD\).

**Reasoning:**

\(AB \,\)is the base of the parallelogram and the perpendicular on \(AB \,\)is \(DL\) (the height). The area of parallelogram is given as \(1470 \,\rm cm^2.\) By using the formula of area of parallelogram we can find the height \(DL\). Similarly, if you take \(AD\) as the base and \(BM\) as perpendicular (height) on \(AD\), again by using the formula of area of parallelogram we can find the length of \(BM\).

**Steps:**

Given, \(AB\)\(= 35 \,\rm cm\), \(BC = 49 \rm \,cm\) and Area \(= 1470 \,\rm cm^2\)

Area of parallelogram ABCD \(=\) Base \((AB)\) \(\times\) Height \((DL)\)

\[\begin{align}1470 &= 35 \times {{DL}}\\{{DL}} &= \frac{{1470}}{{35}}\\{{DL}} &= 42\;\rm cm\end{align}\]

Area of parallelogram ABCD \(=\) Base \((BC)\) \(\times\) Height \((BM)\)

\[\begin{align}1470 &= 49 \times {{BM}}\\{{BM}} &= \frac{{1470}}{{49}}\\{{BM}} &= 30\;\rm cm\end{align}\]