Q4 of 21 Page 72

All red triangles in the picture are equilateral. What is the ratio of the sides of the outer and inner squares?


Let the side of red equilateral triangles be 1m.


In such rectangles, breadth = 1m


And length = (√3/2) + (√3/2) = √3 m (Sum of height of red triangle)


Side of outer square = (√3 + 1) m


Side of inner square = (√3 – 1) m


∴ Ratio of side of outer to inner squares =


More from this chapter

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2

A square and an equilateral triangle of sides twice as long are cut and the pieces are rearranged to form a trapezium, as shown below:


If a side of a square is 2 centimetres, what are the area and perimeter of the trapezium?


 3

Calculate the perimeter and area of the triangle in the picture.


 5

From the pair of numbers given below, pick out those whose product is a natural number or a fraction:

(i) √3, √12


(ii) √3, √1.2


(iii) √5, √8


(iv) √0.5, √8


(v) ,


1

Calculate the length of the sides of the equilateral triangle on the right, correct to a millimetre.