Question

in a parallelogram is one third of its base. if the area of the parallelogram is 192cm square, find its base and height​

Answer 1

Correct question:

• In a parallelogram height is one third of its base. if the area of the parallelogram is 192cm square, find its base and height?

GivEn:

• The area of the parallelogram is 192cm square.
• The height is one third of its base.

To find:

• Its base and height?

Solution:

☯ Let base of parallelogram be b cm.

Then, height of parallelogram will be 1/3b cm

Now,

★ According to the Question:

As we know that,

✮ Area of parallelogram = bh

⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀

Therefore,

➻ b × 1/3b = 192

➻ b × 1b = 192 × 3

➻ b² = 576

➻ √b = √576

➻ b = 24cm

Hence,

• Base of parallelogram, b = 24 cm
• Height of parallelogram, 1/3b cm = 1/3 × 24 = 8cm

⠀⠀━━━━━━━━━━━━━━━━━━━━━

✮ More to know:

• A = b × h
• Area using trigonometry = ab sin (x)
• Area using diagonals = ½ × d1 × d2 sin (y)
• Area of square = side × side
• Perimeter of square = 4 × side
• Diagonal of rectangle = √2 × side

Answer 2

Appropriate Question :-

In a parallelogram the height of the given parallelogram is one third of its base. If the area of the parallelogram is 192cm², find its base and height.

Given :-

Height of a Parallelogram is One third of it's Base and the area of the parallelogram is 192 cm².

To Find :-

Base and Height of the Parallelogram .

Used Concepts :-

Area of a Parallelogram i.e " b × h " . Where 'b' is the base and 'h' the height of the Parallelogram .

A identity i.e a² - b² = ( a + b ) ( a - b )

Solution :-

Let , Base of the Parallelogram = ( b ) = x cm

Now , Height of the Parallelogram = ( h ) = x/3 cm

According to the Question :-

Area of given parallelogram = 192 cm²

b × h = 192 cm²

Put the values of b and h respectively :-

$x \times \frac{x}{3} = 192$

${x}^{2} = 192 \times 3$

${x}^{2} = 576$

${x}^{2} - 576 = 0$

${x}^{2} - ( {24)}^{2}$

Now , we will apply the identity which is discussed above :-

$(x + 24)(x - 24) = 0$

Either , x + 24 = 0 or x - 24 = 0

x = 24 , -24 cm

But length can't be measured '>0' . Therefore, we neglect the -ve value and get the Base of the Parallelogram as x = 24 cm .

Now, Height of the Parallelogram = h = x / 3 = 24 /3 = 8 cm .

Therefore, height of the given parallelogram is 8mc and base is 24 cm .

Verification :-

b × h = 192

24 × 8 = 192

192 = 192

Henceforth , Verified !