Question

The base of a parallelogram is 3 time of its corresponding height. if the area of the parallelogram is 48 sq cm, then find the base and the corresponding height of the parallelogram

Answer 1

✬ Base = 12 cm ✬

✬ Height = 4 cm ✬

Step-by-step explanation:

Given:

• The base of a parallelogram is 3 times of its height.
• Area of the parallelogram is 48 cm².

To Find:

• What is the measure of height and base of parallelogram ?

Solution: Let the meaure of height of parallelogram be h cm. Therefore,

➟ Base of ||gm = 3 times of height

➟ Base = 3h cm

As we know that the :-

★ Area of ||gm = ( Base $\times$ Height ) ★

According to the question

• Area = 48 cm²

$\implies{\rm }$ 48 = ( Base $\times$ Height )

$\implies{\rm }$ 48 = ( 3h $\times$ h )

$\implies{\rm }$ 48 = 3h²

$\implies{\rm }$ 48/3 = h²

$\implies{\rm }$ 16 = h²

$\implies{\rm }$ √16 = h

$\implies{\rm }$ √4 $\times$ 4 = h

$\implies{\rm }$ 4 cm = h

So,

➯ Height of ||gm = h = 4 cm

➯ Base of ||gm = 3h = 3(4) = 12 cm

________________________

★ Verification ★

➛ 48 = (Base)(Height)

➛ 48 = (12)(4)

➛ 48 = 48

[ Verified ]

Answer 2

GIVEN:

• The base of a parallelogram is 3 time of its corresponding height.
• Area of the parallelogram is 48 sq cm.

TO FIND:

• What is the base and the corresponding height of the parallelogram ?

SOLUTION:

Let the base of Parallelogram be 'b' cm and height be 'h' cm

According to question:-

☞ The base of a parallelogram is 3 time of its corresponding height.

$\bf{\dashrightarrow b = 3h...1)}$

We know that the formula for finding the area of parallelogram is:-

$\large\bf{\star \: Area = Base \times Height\: \star}$

According to question:-

On putting the given values in the formula, we get

$\rm{\dashrightarrow 48 = 3h \times h}$《From equation 1)》 

$\rm{\dashrightarrow 48 = 3 h^2 }$

$\rm{\dashrightarrow \cancel\dfrac{48}{3} = h^2 }$

$\rm{\dashrightarrow 16 = h^2 }$

$\rm{\dashrightarrow \sqrt{16} = h }$

$\bf{\dashrightarrow \star \: 4 \: cm = h \: \star}$

Put the value of 'h' in equation 1)

$\rm{\dashrightarrow b = 3 \times 4 }$

$\bf{\dashrightarrow \star \: b = 12 \: cm \: \star }$

❝ Hence, the base of the Parallelogram is 12 cm and height of the Parallelogram is 4 cm ❞

__________________

VERIFICATION:

Put the values in the formula:

➻ $\bf{ 48 = 12 \times 4}$

➻ $\bf{ 48 = 48}$

$\rm{[L.H.S. = R.H.S.]}$

VERIFIED....