Question

The perimeters of a rhombus and square are equal to 52 cm. If one of the diagonals of the rhombus is 10 cm, find the difference in their areas.​

Answer 1

Answer:

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Answer 2

Question:-

The perimeters of a rhombus and square are equal to 52 cm. If one of the diagonals of the rhombus is 10 cm, find the difference in their areas.​

Given:-

• Perimeter of a rhombus.

• Perimeter of a square.

To Find:-

• The difference in their areas.

Answer:-

60 cm²

Explanation:-

Perimeter of a rhombus = perimeter of a square

=4×side = 52

Side=52÷4= 13 cm

Note: We know that the diagonals of a rhombus bisect each other at right angles.

In right triangle ABC:

OA = ½×AC = ½×10 =5 cm

OB= √AB²-OA²

OB=√(13)²-(5)²

OB=√169-25

OB=√144= 12 cm

BD= ( 2×OB) cm = (2×12) cm = 24 cm

Area of a rhombus= ½× product of its diagonals

= ½× AC×BD = ½×10× 12= 60 cm²