Question

Q.3 The base of a parallelogram is twice its height. If the area of the
parallelogram is 512 cm’, find the base and height of the parallelogram.​

Answer 1

Step-by-step explanation:

length height of parallelogram be x

then base will be 2x

area of parallelogram = b × h

512 = 2x × x

512 = 2x sq.

512/2 = x sq.

256 = x sq.

root 256 = x

16 = x

hence height = 16 cm

base = 2x = 2 × 16

= 32 cm

Answer 2

Given :

• Base of parallelogram is twice it's height.
• Area of Parallelogram = 512cm²

To Find :

• Base and height of Parallelogram.

Solution :

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

As the base of parallelogram is twice it's height. So,

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

Using Formula :

$\boxed{Area\:of\:Parallelogram=Base\times{Height}}$

Putting Values :

$\longmapsto\tt{512=2x\times{x}}$

$\longmapsto\tt{512={2x}^{2}}$

$\longmapsto\tt{\cancel\dfrac{512}{2}={x}^{2}}$

$\longmapsto\tt{\sqrt{256}={x}^{2}}$

$\longmapsto\tt\bold{x=16}$

So , The value of x is 16..

Now :

$\longmapsto\tt\bold{Height=16cm}$

$\longmapsto\tt{Base=2(16)}$

$\longmapsto\tt\bold{32cm}$

_______________________

VERIFICATION :

$\longmapsto\tt{Base\times{Height}=512}$

$\longmapsto\tt{32\times{16}=512}$

$\longmapsto\tt\bold{512=512}$

HENCE VERIFIED