Question

Q3. The altitude of a parallelogram is one third of the base. If the area is 243 cm find its altitudes.​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Altitude of Parallelogram is $\huge\bold{ 9 \:cm}$

Given:

Altitude of a parallelogram is one third of the base and area of parallelogram is 243 cm^2

To Find :

Altitude of the parallelogram

Some properties of parallelogram:

1. Parallelogram is a Quadrilateral having four sides and four vertex.
2. It's opposite sides are equal and parallel.
3. Opposite angles are also equal.
4. The sum of the square of all sides is equal t to the sum square of Diagonals.

Now ,

Area of parallelogram is : $\sf Base \times height$

According to the Question :

Let the base be 'x' cm

and altitude be 1/3 of x=x/3cm

$\sf= > x \times \dfrac{x}{3} = 243$

$\sf = > \dfrac{ {x}^{2} }{3} = {3}^{5}$

$\sf= > {x}^{2} = {3}^{6}$

$\sf= > {x}^{2} = 3 \times 3 \times 3 \times 3 \times 3 \times 3$

$\sf= > {x}^{2} = 729$

$\sf= > x = \sqrt{729} = 27$

$\therefore$The base is 27 cm

and Altitude is x/3=27/3=9cm

Base of parallelogram =27cm

Altitude of parallelogram =9cm

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Altitude of Parallelogram is $\huge\bold{ 9 \:cm}$

Given:

Altitude of a parallelogram is one third of the base and area of parallelogram is 243 cm^2

To Find :

Altitude of the parallelogram

Some properties of parallelogram:

Parallelogram is a Quadrilateral having four sides and four vertex.

It's opposite sides are equal and parallel.

Opposite angles are also equal.

The sum of the square of all sides is equal t to the sum square of Diagonals.

Now ,

Area of parallelogram is : $\sf Base \times height$

According to the Question :

Let the base be 'x' cm

and altitude be 1/3 of x=x/3cm

$\sf= > x \times \dfrac{x}{3} = 243$

$\sf = > \dfrac{ {x}^{2} }{3} = {3}^{5}$

$\sf= > {x}^{2} = {3}^{6}$

$\sf= > {x}^{2} = 3 \times 3 \times 3 \times 3 \times 3 \times 3$

$\sf= > {x}^{2} = 729$

$\sf= > x = \sqrt{729} = 27$

$\therefore$The base is 27 cm

and Altitude is x/3=27/3=9cm

Base of parallelogram =27cm

Altitude of parallelogram =9cm