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1.

The base and corresponding altitude of aparallelogram are 10 cm and 12 cm respectively. If the other altitude is 8cm, find the length of the other pair of parallel sides.

Answer» Area of parallelogram=>`B xx H`
where B and H are base and height of parallelogram.
`b_1xxh_1=b_2xxh_2`
`10xx12=8=xxb_2`
`b_2=15cm`
Discussion
2.

The area of a rhombus id `144 c m^2`and one of its diagonal is double the other.The length of the longer diagonal is(a)12 cm (b) 16 cm(c)18 cm (d) 24 cm

Answer» Area of rhombus=`1/2` x product of diagonals
let `d_1=d and d_2=2d`
substituting in the formula we get=>`1/2 xx d xx 2d=144`
=>`d=+-12` rejecting negative sign as side cannot be negative.
length of diagonals are 12cm and 24 cm.
Discussion
3.

The base of an isosceles triangle is 12 cmand its perimeter is 32 cm. Find its area.

Answer» Let the length of the two equal sides be x.
Perimeter of triangle=`32=2x+12`
=>`x=10`
Area of triangle=`sqrt(s(s-a)(s-b)(s-c))` where s is the semiperimeter of triangle
`s=32/2=16`
`sqrt(16xx6xx6xx4)=4 xx 6xx 2=48(cm)^2`
Discussion