The perimeter of a parallelogram is 60 cm and the ratio of its adjacent sides is 3:2. If the altitude corresponding to the largest side of the parallelogram is 5 cm. Find the area of the parallelogram and the altitude corresponding to the smaller side.

Given:

The perimeter of a parallelogram is 60 cm and the ratio of its adjacent sides is 3:2.

The altitude corresponding to the largest side of the parallelogram is 5 cm.

To do:

We have to find the area of the parallelogram and the altitude corresponding to the smaller side.

Solution:

Let one side be $3x$ and the adjacent side $2x$.

Perimeter of the parallelogram $=3x+2x+3x+2x$

$60=10x$

$x=\frac{60}{10}$

$x=6\ cm$

This implies,

Larger side $=3x=3(6)=18\ cm$

Smaller side $2x=2(6)=12\ cm$

Area of parallelogram $=$ Larger side $\times$ Altitude corresponding to the larger side.

$=18\times5$

$=90\ cm^2$

Let h be the altitude corresponding to the smaller side.

Area of parallelogram $=$ Smaller side $\times$ Altitude corresponding to the smaller side.

$90=12\times h$

$h=\frac{90}{12}\ cm$

$h=7.5\ cm$

The altitude corresponding to the smaller side is 7.5 cm.

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