Question

The base and height of a parallelogram are in the ratio 5:6. It's area is 1470 square units. Find the base and height of the figure.

Answer 1

As per the data given in the question,

We have to calculate the base and height of the parallelogram.

As per question,

it is given that,

Ratio of base and height = 5 :6

Area of parallelogram = 1470 square unit.

As we know that,

Area of parallelogram $= base \times height$

So, let the base of the parallelogram = 5x

Height of parallelogram = 6x

So, from above formula,

We can write it as,

$(5x \times 6x) = 1470\\=>30x^2 = 1470\\=>x^2 = \frac{1470}{30}\\=>x^ 2 = 49\\=>x = {\sqrt{49}} = 7\:unit$

Hence, the base of parallelogram will be $= 5x = (5\times 7) = 35\:units$

Hence, the base of parallelogram will be $=6x = (6\times 7) = 42\:units$

Hence, base of the parallelogram will be of 35 units while the height of parallelogram will be 42 units.

Answer 2

Here the ratio of base and height of a parallelogram is given to br 5:6

Also, the area of the parallelogram is given to be 1470 square units

Let the base and height be 5x and 6x

Then, area of parallelogram = base × height

1470 = 5x × 6x

1470 = 30 x²

x² = 49

x = 7

So, 5x = 5 × 7

= 35

6x = 6 × 7

= 42

Hence, the base and height will be 35 unit and 42 unit respectively.