Q4 of 16 Page 153

A 68-centimeter-long rope is used to make a rhombus on the ground. The distance between a pair of opposite corners is 16 meters.

i) What is the distance between the other two corners?


ii) What is the area of the ground bounded by the rope?

68-centimeter-long rope is used to make a rhombus

The above statement states that perimeter of the rhombus is 68 cm.


And they have given that diagonal (d1) is 16 cm


(In question they have given that as meter that should be a meter)


Perimeter = 4 × a


Where,


a = side of the rhombus.


68 = 4a


a = 17 cm



From the triangle AOD


AD2 = AO2 + OD2


172 = 82 + X2


X = √(289-64)


= 15


(i) The distance between the other two corners (d2) = 2X


= 2 × 15


= 30 cm


(ii)The area of the rhombus = × ×


= × ×


= 60 cm2


More from this chapter

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2

Draw a non-square rhombus of area 9 square centimetres.

 3

The area of a rhombus is 216 square centimetres and the length of one of its diagonals is 24 centimetres. Compute the following measurements of this rhombus.

i) Length of the second diagonal


ii) Length of a side


iii) Perimeter


iv) Distance between sides

 5

In the figure, the midpoints of the diagonals of a rhombus are joined to form a small quadrilateral:


(i) Prove that this quadrilateral is a rhombus.


(ii) The area of the small rhombus is 3 square centimetres. What is the area of the large rhombus?

 6

What is the area of the largest rhombus that can be drawn inside a rectangle of sides 6 centimetres and 4 centimetres?