Question

the height of a parallelogram is two third of its base and the area of parallelogram is 864cm square. find its height and base​

Answer 1

Given:

The height of a parallelogram is two-third of its base

The area of the parallelogram is 864 cm sq.

To find:

The base and height of the parallelogram

Now,

The formula to find the area of the parallelogram is

$\boxed{\bf =base \times height \ unit\ sq.}$

Also,

According to the question,

The height of the parallelogram is two-third of its base,

Let the base be x cm

So, the height of the parallelogram will be 2/3 of x = 2x/3 cm

Now,

Putting the given values,

Area = base * height

⇒ 864 = x * 2x/3

⇒ 864 = 2x²/3

⇒ 864 × 3 = 2x²

⇒ 2592 = 2x²

⇒ 2592 ÷ 2 = x²

⇒ 1296 = x²

⇒ 36 = x

Thus,

The length of the base is x cm = 36 cm

And the length of the height is 2x/3 = (2*36)/3 = 72/3 = 24 cm

Answer 2

Given :-

Height = 2/3 of its base

Area = 864 cm²

To Find :-

Height and base

Solution :-

Let

Height = 2x/3

Base = x

$\sf Area = b\times h$

$\sf 864 = \dfrac{2x}{3} \times x$

$\sf 864 = \dfrac{2x^2}{3}$

$\sf 864(3) = 2x^2$

$\sf 2592 = 2x^2$

$\sf \dfrac{2592}{2} =x$

$\sf 1296 = x^{2}$

$\sf 36 =x$

Height = 2/3 × 36 = 2 × 12 = 24 cm

Base = 36 cm