Question

the perimeter of a rhombus is 40 cm if one diagonal is 16m find 1. it's another diagonal 2. area

Answer 1

First of all we will find length of side of rhombus by using formula
the perimeter of rhombus = 4 * sides
40 = 4 * sides
10 cm = side of rhombus
now we know that diagonal of rhombus are perpendicular bisectors of each other hence by using Pythagoras theorem
(10)squared = (8)squared + (x)squared
6 cm = x
12 cm is length of other diagonal .....(6 * 2)=12 cm
Now area of rhombus = 1/2 * product of length of diagonals
= 1/2 * 16 *12
=96 sq.cm
length of other diagonal is 12 cm and area of rhombus is 96 sq.cm

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Answer 2

Let, l = other diagonal
Then, halfxlsq. = (10sq. - 8sq. )
=> halfxlsq. = 36
=> halfxl = 6
=> l = 6x2 = 12cm
Therefore, the other diagonal = 12cm
And area = half x d1 x d2
= half x 16 x 12 = 96 sq.cm