Question

Problem Description - 2
The area of a parallelogram is 72 square centimetre and its altitude is twice the corresponding base. What
Correct answer: +1
Incorrect answer: 0
Options
8 centimetre
O 7 centimetre
© 12 centimetre
6 centimetre
S Clear Answer​

Answer 1

Given that:

• The area of a parallelogram is 72 sq.cm and its altitude is twice the corresponding base.

Options:

• a) 8 cm
• b) 7 cm
• c) 12 cm
• d) 6 cm

To find:

• base of parallelogram

Required Formula:

• Area of parallelogram = b × h

Solution:

❍ Let the base be x cm and height be 2x cm respectively.

Then,

$\\ :\implies\sf{72 = x \times 2x} \\ \\ :\implies\sf{72 = 2 {x}^{2} } \\ \\ :\implies\sf{ \frac{ \cancel{72}}{ \cancel{2}} = {x}^{2} } \\ \\ :\implies\sf{36 = {x}^{2} } \\ \\ :\implies\sf{x = \sqrt{36} } \\ \\ :\implies\underbrace{ \boxed{ \mathfrak{x = 6}}} \: \green{ \bigstar}$

Therefore,

• base = x = 6 cm
• height(altitude) = 2x = 2 × 6 = 12 cm

Hence,

• The base of parallelogram is 6 cm and option(d) is correct.

━━━━━━━━━━━━━━━

Verification:

Let us put the value of x in the given formula,

$\\ :\implies\sf{72 = 6 \times( 2 \times 6)} \\ \\ :\implies\sf{72 = 6 \times 12} \\ \\ :\implies\sf{72 = 72}$

• Hence,Verified.

Answer 2

Given:

The area of a parallelogram is 72 sq.cm and its altitude is twice the corresponding base.

To find:

Base of parallelogram

Formula:

Area of parallelogram = b × h

Let's Solve:

Let the base be x cm and height be 2x cm respectively.

Then,

$\implies \rm{72=x×2x}$

$\implies \rm{72=2x²}$

$\implies \rm{72/2=x²}$

$\implies \rm{36=x²}$

$\implies \rm{x = \sqrt{36} }$

$\implies \rm{x=6}$

Therefore,

▪︎Base = x = 6 cm

▪︎Height(altitude) = 2x = 2 × 6 = 12 cm

Hence,

• The base of parallelogram is 6 cm and option(d) is correct.

Thank you!!

@itzshivani