Question

The garden is in the shape of a rhombus ,whose perimeter is 60m.If the length of one diagonal is 18m,find the length of the other diagonal.

Answer 1

Answer:

24 m

Step-by-step explanation:

see attachment for diagram

in rhombus all sides are equal

so AB = BC  = CD = AD

but perimeter = 60 m

=> AB + BC + CD + AD = 60 m

=> AB + AB + AB + AB = 60       [ all sides are equal ]

=> 4AB = 60

=> AB = 60 / 4 = 15

so AB = BC = CD = AD = 15 m

in rhombus, diagonals bisect each other at right angles

let diagonal 1 be AC and diagonal 2 be BD

AC = 18 m [ given ]

let intersection of two diagonals AC and BD be O

so BD = 2 x DO [ diagonals bisect each other ]

and  AO = CO = 18/2 = 9

but AO² + DO² = AD²       [ right triangle - pythagoras theorem ]

=> 9² + DO² = 15²

=> 81 + DO² = 225

=> DO² = 225 - 81 = 144

=> DO = $\sqrt{144}$ = 12 m

BD = 2  x DO

= 2 x 12 = 24 m

so length of other diagonal is 24 m

Answer 2

Answer:

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Step-by-step explanation:

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