Question

The height of a parallelogram is one third of its base if the area of the parallelogram is 108 CM square find its base and height

Answer 1

The height of a parallelogram is one third of its base. If the area of the parallelogram 192 cm², what is its height and base?

Let the base of the parallelogram be b, so that the height becomes (b/3), so we have

b*(b/3) = 192, or

b^2 = 192*3 = 576, or

b = 576^0.5 = 24.

So the base is 24 cm and the distance between the opposite sides in 8 cm.

Answer 2

$\huge{given}$

• The height of a parallelogram is one-third of its base.
• Area of parallelogram = 108cm²

$\huge{To \: find -}$

• Height and base.

$\huge{Solution -}$

Here, we are given with the area of the parallelogram, and it's height is 1/3 of it's base, and we need to find the height and base. For that we will use the formula of area of parallelogram, and will solve the further calculations.

So -

Let the height be termed as x

Therefore, base will be 1/3x

Area is 108cm²

Now -

Area of parallelogram = B × H

where -

• B = base

• H = Height

On substituting the values -

Area = B × H

$\longrightarrow \sf\dfrac{1}{3}$

x × x = 180cm²

x² = 108cm²

$\longrightarrow \: x² = 108 × 3 \\\longrightarrow x² = 324 \\ \longrightarrow x = \sf\sqrt{324}$

$\longrightarrow x = 18 cm$

Similarly -

$\longrightarrow Height = \sf\dfrac{1}{3}$

$\longrightarrow Height = 6 cm$

❝Verification -❞

Area = B × H

108cm² = 18 cm × 6 cm

108cm² = 108cm²

therefore∴

Height and base of the parallelogram is 18 cm and 6 cm

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