Question

6. The ratio of base & height of parallelogram are 2:1 and area of parallelogram is 1250 cm 2 . Then find the base & height of a parallelogram.



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Answer 1

Question:-

The ratio of base & height of parallelogram are 2:1 and area of parallelogram is 1250 cm² . Then find the base & height of a parallelogram.

Answer:-

• The base and height of parallelogram are 50 cm and 25 cm.

To find:-

• Base and height of parallelogram

Solution:-

• Ratio = 2:1
• Area of parallelogram = 1250 cm²

Let,

• Base of parallelogram = 2x
• Height of parallelogram = x

As we know,

$\large{ \boxed{ \huge{ \mathfrak{area = b \times h}}}}$

Where,

• b = base of parallelogram
• h = height of parallelogram

According to question,

$\large{ \rm: \implies \: \: \: \: \: \: \: \: 2x \times x = 1250}$

$\large{ \rm: \implies \: \: \: \: \: \: \: \: 2 {x}^{2} = 1250}$

$\large{ \rm: \implies \: \: \: \: \: \: \: \: {x}^{2} = \frac{1250}{2} }$

$\large{ \rm: \implies \: \: \: \: \: \: \: \: {x}^{2} = 625}$

$\large{ \rm: \implies \: \: \: \: \: \: \: \: x = \sqrt{625} }$

$\large{ \rm: \implies \: \: \: \: \: \: \: \: x = 25}$

• The value of x is 25 cm

Now,

• Base of parallelogram = 2x = 50 cm
• Height of parallelogram = x = 25 cm

Hence,

The base and height of parallelogram are 50 cm and 25 cm.

Answer 2

$\large\purple{\boxed{\sf{Answer}}}$

Given,

Ratio = $\normalsize\mathsf{2:1}$

Area = $\normalsize\mathsf{{1250cm}^{2}}$

To find,

Base and Height of Parallelogram

Solution,

Let Base be "2x" and Height be "x"

So,

$\normalsize\pink{\boxed{\sf{Area\: of\: parallelogram=Base×Height}}}$

Therefore,

$\normalsize\mathsf{{1250cm}^{2}}$=$\normalsize\mathsf{(2x) × (x)}$

$\mathsf{{1250cm}^{2}}$ = $\mathsf{{2x}^{2}}$

$\mathsf{{x}^{2}}$=$\mathsf{ \frac{1250cm}{2} }$

$\mathsf{{x}^{2}}$= $\mathsf{625}$

$\mathsf{x}$ = $\mathsf{ \sqrt{625} }$

$\large\orange{\boxed{\sf{x=25}}}$

➡Base = 25cm

➡Height = 50cm

Hope it helps..

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