Question

A rhombu~ s~et whose perimeter is 260cm and whose one diagonal is 66c~ %inted on both the sides at the rate of 50 paise per cm 2 . Find

Answer 1

Answer:

Step-by-step explanation:

Perimeter of a Rhombus=4×one of the side

                           260cm=4×side

                        260cm÷4=side

                              65cm=side

Let the rhombus be named as ABCD let the diagonals bisect at O.

AB=BC=CD=DA=65cm(All sides of a rhombus are equal)

One of the diagonal=AC=66cm.

Then, AO=66cm÷2=33cm

Then, diagonal BD=???

Since the diagonals of a rhombus bisect each other at Right angles, then we can use the Pythagoras Property to find the other diagonal.

By Pythagoras Property,

Hypotenuse²=Base²+Altitude²

Base²=Hypotenuse²-Altitude²

OD²=AD²-AO²

OD²=65²-33²    [Using a²-b²=(a+b)(a-b)]

OD²=(65+33)(65-33)

OD=√98-32

OD=√64

OD=8cm

Then, BD=OD×2

               =8×2

               =16cm

Area of a rhombus=d1×d2

                              =16cm×66cm

                              =1056cm²

Then the cost per 1cm²=50 paise÷100=Rs 0.5

Then the cost per 1056 cm²=1056×0.5

                                              =Rs528

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