Question

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

Verified
147.6k+ views
Hint: Frame an equation from the information given in the question and then use formula,
Area of parallelogram =Base* Height.

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.