Question

Find the area of a rhombus whose perimeter is 200m and one of the diagnols is 80m.

Answer 1

Here is a solution
: -

The side length is = 200/4 = 50m


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If x and y are half of the lengths of the diagonals


Then the formula is √(x^2 + y^2)
= 50 x^2 + y^2 = 2500

In given, one of the diagonals is 80m,


then half of the diagonal is 40m 40^2 + y^2 = 2500 1600 + y^2
= 2500 y^2
= 900
y = 30,


So another diagonal is 60m




Therefore area of the rhombus 30*80 is 2400 m^2.





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copied from the book of shrinivas ramanujan book.

Answer 2

perimeter=200/4=50m
half diagonal =80/2=40mtr
then using Pythagoras theorem we can find other diagonal half part
x²=50²-40²
=2500-1600
=900
x=30mtr
full length of diagonal=30×2=60mtr

area=1/2×product of diagonal
=1/2×60×80
=2400mtr²