Question

Question 89

Perimeter of a parallelogram-shaped land is 96 m and its area is $270m^2$. If one of the side of this parallelogram is 18 m, find the length of the other side. Also, find the lengths of altitudes l and m in the given figure.

Answer 1

Given, perimeter of parallelogram = 96 m and area of parallelogram $=270m^2.$
In a parallelogram ABCD, AB = CD = 18 m and AD = BC

As we know, perimeter of a parallelogram ABCD = AB + BC + CD + AD
$\Rightarrow 96=18+AD+18+AD[\because$ AD=BC]
$\Rightarrow 96=36+2AD\Rightarrow 2AD=60\Rightarrow AD=30m$
So, AD = BC = 30 m
Now, area of parallelogram ABCD = Base $\times$ Corresponding height
$\Rightarrow 270=AB\times DE[\because base=AB]\Rightarrow 270=18\times DE\Rightarrow \frac{270}{18}=DE\Rightarrow DE=m=15m$
Also, area of parallelogram $ABCD=AD\times BF[\because$ base =AD]
$\Rightarrow 270=30\times l\Rightarrow BF=l=\frac{270}{30}\Rightarrow l=9m$
Hence, altitudes l = 9 m and m =15 m.