Question

Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio (A) 2 : 3 (B) 4 : 9 (C) 81 : 16 (D) 16 : 81

Answer 1

Assume that the two similar triangles are equilateral triangles.
give that the ratio of two triangles are 4:9(in this problem we can take 4 as side of equilateral triangle & 9 as one side of another equilateral triangle)

Now we find area of equilateral triangle.
Formula for AREA of equilateral triangle is √3/4a.a [√3/4 a square]
(In equilateral triangle, all sides are equal)


first equilateral triangle's area is
√3/4×4×4 (its side is 4)
√3/4×16(cancel the numerator 16 and denominator 4) we get
4√3


second equilateral triangle's area is
√3/4×9×9(its side is 9)
√3/4×81

Then we find the ratio of two equilateral triangles.
4√3 : 81√3/4
cancel √3 on both sides we get
4/1 : 81/4 (we know that 4 = 4/1)

for reducing fraction we can multiply

the numerator of first triangle that is 4 and denominator of second triangle that is 4 &
the numerator of second triangle that is 81 and denominator of first triangle that is 1
4×4 : 81×1
16 : 81
so the area of two similar triangles ratio are 16 : 81