0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

In the given figure, a ABC has been given in which AB = 7.5 cm, AC = 6.5 cm and BC = 7cm. On base BC, a parallelogram DBCE of the same area as that of ABC is constructed. Find the height DL of the parallelogram.

Solution
Verified by Toppr

Consider $$\Delta$$ ABC
It is given that AB = 7.5cm, BC = 7cm and AC = 6.5cm
Take a = 7.5cm, b = 7cm and c = 6.5 cm
So we get
$$s=\dfrac{a+b+c}{2}$$
$$s=\dfrac{7.5+7+6.5}{2}$$
By division
s=10.5cm
We know that
Area=$$\sqrt{s(s-a)(s-b)(s-c)}$$
By substituting the values
Area=$$ \sqrt{10.5(10.5-7.5)(10.5-7)(10.5-6.5)}$$
So we get
Area=$$ \sqrt{10.5\times3\times3.5\times4}$$
It can be written as
Area=$$\sqrt{441}$$
By multiplication
Area=$$21cm^2$$
We know that the area of parallelogram DBCE = Area of $$\Delta$$ ABC
It can be written as
$$BC\times DL = 21$$
By substituting the values
$$7 \times DL = 21$$
By division
DL = 3cm
Therefore, the height DL of the parallelogra

Was this answer helpful?
10
Similar Questions
Q1
In the figure, ABC has sides AB=7.5cm,AC=6.5cm and BC=7cm. On base BC a parallelogram DBCE of same area as that of ABC is constructed. Find the height DF of the parallelogram in cm?
78135.jpg
View Solution
Q2
In the given, ΔABC has sides AB=7.5 cm,AC=6.5 cm and BC=7 cm. On base BC a parallelogram DBCE of same area as that of ΔABC is constructed. Find the height DF of the parallelogram.
244973_caf6fcc1890841d394abbb81d0d700c7.png
View Solution
Q3
In the figure, ΔABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7cm. On base BC a parallelogram DBCE of same area as that of ΔABC is constructed. Find the height DF of the parallelogram.


View Solution
Q4
Question 6
In the figure, ΔABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7cm. On base BC a parallelogram DBCE of same area as that of ΔABC is constructed. Find the height DF of the parallelogram.

View Solution
Q5
In the given figure, a ∆ABC has been given in which AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC, a parallelogram DBCE of the same area as that of ∆ABC is constructed. Find the height DL of the parallelogram.
View Solution