Question

A rhombus shaped field has green grass for 18 cows to grace. If each side of the rhombus is 30 m and it's longer diagonal is 48m, how much area of grass field will each cow be getting

Answer 1

ʜᴇʟʟᴏ ᴍᴀᴛᴇ!

As given in figure,

Area of 1 triangle by Heron's Formula
√[ s( s - a )( s - b )( s - c ) ], where
s = ( a + b + c )/2

s = ( 48 + 30 + 30 )/2
= 108/2 = 54 m

√[ 54( 54 - 48 )( 54 - 30 )( 54 - 30 ) ]
√ [ 2 × 3³ × 2 × 3 × 2³ × 3 × 2³ × 3 ]
( 3 × 3 × 3 × 2 × 2 × 2 × 2 ) m² = 432 m²

Area if whole Rhombus = 432 m² × 2
= 864 m²

So, each cow will grace = 864 m²/ 18
= 48 m²

Hence, each cow will grace 48 m².

Hope it helps

Answer 2

We know that the diagonals of the rhombus bisects each other at 90°

So, By Pythagoras Theorem,


( half of first diagonal )² + ( half of second diagonal )² = side²



=> ( 48/2 )² + ( half of second diagonal )² = 30²



=> 24² + ( half of second diagonal )² = 30²


=> 576 + ( half of second diagonal )² = 900


=> ( half of second diagonal )² = 324


=> half of second diagonal = √324 = 18


=> second diagonal = 2 × 18 = 36 m





Now,

Area of rhombus = product of diagonals × 0.5

=> Area of rhombus = 48 × 36 × 0.5

=> Area of rhombus = 24 × 36

=> Area of rhombus =864 m²



To know the area which will be covered by each cow, Divide the area of rhombus by the number of cows


=> Area covered by cows = 864 / 18

=> Area covered by cows = 48 m²




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