Question

Question No. 19
The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, then find its
height.​

Answer 1

Given :

• Base of a parallelogram is twice its Height .
• Area of Parallelogram is 72 cm² .

To Find :

• Height of Parallelogram .

Solution :

$\longmapsto\tt{Let\:Height\:be=x}$

As Given that Base of a parallelogram is twice its Height . So ,

$\longmapsto\tt{Base=2x}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Parallelogram=b\times{h}}$

Putting Values :

$\longmapsto\tt{72=2x\times{x}}$

$\longmapsto\tt{72=2{x}^{2}}$

$\longmapsto\tt{\cancel\dfrac{72}{2}={x}^{2}}$

$\longmapsto\tt{36={x}^{2}}$

$\longmapsto\tt{\sqrt{36}=x}$

$\longmapsto\tt\bf{6=x}$

Therefore :

$\longmapsto\tt{Height\:of\:Parallelogram=x}$

$\longmapsto\tt\bf{6\:cm}$

$\longmapsto\tt{Base\:of\:Parallelogram=2(6)}$

$\longmapsto\tt\bf{12\:cm}$

_______________________

VERIFICATION :

$\longmapsto\tt{72=2x\times{x}}$

$\longmapsto\tt{72=2(6)\times{6}}$

$\longmapsto\tt{72=12\times{6}}$

$\longmapsto\tt\bf{72=72}$

HENCE VERIFIED

Answer 2

Answer:

6 cm

Step-by-step explanation:

$\underline{\bigstar\:\textsf{Given:}}$

• Base of a parallelogram is twice its height.
• Area of parallelogram = 72 cm²

$\underline{\bigstar\:\textsf{To\:find:}}$

• Its height = ?

$\underline{\bigstar\:\textsf{Solution:}}$

First, let the height be h.

Now, it is saying "The base of a parallelogram is twice its height."

$\implies$ Base = 2h

We remember the area of a parallelogram i.e, $\blue{\sf{base\:\times\:height}}$

(We are given with the area too, put the values to find h)

$\implies$ 72 = 2h × h

$\implies$ 72 = 2h²

$\implies\:\sf{\dfrac{72}{2}\:=\:h^2}$

$\implies\:\sf{\sqrt{36}\:=\:h}$

$\implies$ 6 = h

$\sf{\underline{\boxed{\large{\mathsf{\therefore \:It's\:height\:is\:6\:cm}}}}}$

Hope it helped you dear...