Question

the ratio of base in parllelogram is 3:2 if its area is 384cm2 find its base and height

Answer 1

Corrected Question:

• The ratio of the base and height in a parallelogram is 3 : 2. If the area of the parallelogram is 384 cm², find it's base and height.

Answer:

• Base = 24 units
• Height = 16 units

Steps:

We know that, the formula for calculating the area of a Parallelogram is given as:

→ Area = Base × Height

Let us assume the Base of the parallelogram to be 3x and the Height of the parallelogram to be 2x. Hence we get the Area to be:

→ Area = 3x × 2x

⇒ Area = 6x²

We are given that, the Area of the Parallelogram is 384 cm². Substituting it we get:

→ 384 = 6x²

→ x² = 384 / 6

→ x² = 64

→ x = √64 = ± 8.

But since sides of a parallelogram can't be negative, we can ignore -8.

Hence the value of 'x' is 8.

Hence the measure of base is found to be:

• Base = 3x = 3 × 8 = 24 units.
• Height = 2x = 2 × 8 = 16 units

Answer 2

Question :

The ratio of base and height in parallelogram is 3:2. If its area is 384cm² . Find its base and height.

Answer :

$\sf Given \; that \begin{cases} & \sf{Area \: of \: paralloegram = \bf{384 \: cm^{2}}} \\ & \sf{Ratio \: of \: h \: and \: b = \bf{3:2}} \end{cases}$

$\sf To \; find \begin{cases} & \sf{Base \: of \: paralloegram} \\ & \sf{Height \: of \: paralloegram} \end{cases}$

$\sf Solution \begin{cases} & \sf{Base \: of \: paralloegram = \bf{24 \: cm}} \\ & \sf{Height \: of \: paralloegram = \bf{16 \: cm}} \end{cases}$

$\sf Using \; concept \begin{cases} & \sf{Area \: of \: paralloegram} \end{cases}$

$\sf Using \; formula \begin{cases} & \sf{Area \: of \: paralloegram = \bf{Base \: \times \: height}} \end{cases}$

$\sf Assumptions \begin{cases} & \sf{Base = \bf{3x \: cm}} \\ & \sf{Height = \bf{2x \: cm}} \end{cases}$

What does the question say ?

• This question says that there is a paralloegram of area = 384 cm² and its base and height are not given means we have to find the base and height of the paralloegram. But it's also given that the base and height are in the ratio of 3:2

Procedure of the question :

• To solve this question we have to use the taken assumptions afterthat finding the area of assumptions we get 6x². Afterwards we have to put the values according to the formula to find area of paralloegram using 6x². [Putting the values.....] we get the value of x afterthat using the value of x we have to multiply 3 by 8 and 2 by 8 then we get our final result that are 24 cm and 16 cm as base and height respectively.

Full solution :

As we take 3x and 2x as assumptions of base and height respectively so we have to find the area of these assumptions. Using formula finding the are we get the following results.

☞ Area = 3x × 2x

☞ Area = 6x²

Now, a according to the question as it already given that area of paralloegram is 384 cm² so putting the values according to this and the area of assumptions we get the following results.

☞ 384 = 6x²

☞ x² = 384/6

☞ x² = 64

☞ x = √64

☞ x = 8

Hence, x = 8

Now, finding the base and height we have to into(×) them as seen below.

• Base of paralloegram = 8 × 3 = 24 cm

• Height of paralloegram = 8 × 2 = 16 cm

More knowledge :

Diagram of paralloegram : See the above attachment to see understand the structure of paralloegram.

What is paralloegram ?

• A plane figure.
• A closed surface.
• A quadrilateral.

Some formulas related to paralloegram.

• Using Base and Height A = b × h

• Using Trigonometry A = ab sin (x)

• Using Diagonals A = ½ × d1 × d2 sin (y)

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