# The height of a parallelogram is three-eighth of its base. If the area of the parallelogram is , find its height and base.

Answer

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Hint: Frame an equation from the information given in the question and then use formula,

Area of parallelogram =Base* Height.

Complete step-by-step answer:

Given that the height of the parallelogram is three-eighth of its base. If b is the base and h is the height of the parallelogram, then we have:

$ \Rightarrow h = \dfrac{3}{8}b .....(i)$

Now, we know that the area of a parallelogram is given as:

$ \Rightarrow $ Area of parallelogram Base Height.

$ \Rightarrow A = b \times h$

Putting the area of parallelogram as from the question and the value of h from equation , we’ll get:

$

\Rightarrow 96 = b \times \dfrac{3}{8}b, \\

\Rightarrow {b^2} = \dfrac{{96 \times 8}}{3}, \\

\Rightarrow {b^2} = 256, \\

\Rightarrow b = 16 \\

$

Putting the value of b back in , we will get:

$

\Rightarrow h = \dfrac{3}{8} \times 16, \\

\Rightarrow h = 6 \\

$

Thus the height and base of the parallelogram are 6 cm and 16 cm respectively.

Note: Area of parallelogram is also calculated using formula:

$ \Rightarrow $ Area of parallelogram $ = \dfrac{1}{2} \times $ height (sum of parallel sides)

We can use any of them as per the data given in the question.

Area of parallelogram =Base* Height.

Complete step-by-step answer:

Given that the height of the parallelogram is three-eighth of its base. If b is the base and h is the height of the parallelogram, then we have:

$ \Rightarrow h = \dfrac{3}{8}b .....(i)$

Now, we know that the area of a parallelogram is given as:

$ \Rightarrow $ Area of parallelogram Base Height.

$ \Rightarrow A = b \times h$

Putting the area of parallelogram as from the question and the value of h from equation , we’ll get:

$

\Rightarrow 96 = b \times \dfrac{3}{8}b, \\

\Rightarrow {b^2} = \dfrac{{96 \times 8}}{3}, \\

\Rightarrow {b^2} = 256, \\

\Rightarrow b = 16 \\

$

Putting the value of b back in , we will get:

$

\Rightarrow h = \dfrac{3}{8} \times 16, \\

\Rightarrow h = 6 \\

$

Thus the height and base of the parallelogram are 6 cm and 16 cm respectively.

Note: Area of parallelogram is also calculated using formula:

$ \Rightarrow $ Area of parallelogram $ = \dfrac{1}{2} \times $ height (sum of parallel sides)

We can use any of them as per the data given in the question.

Last updated date: 30th Sep 2023

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