An equilateral triangle is based on the side of a square of area 64 sq. cm and another on the diagonal of the same square. Find the ratio of their areas.

Asked by Topperlearning User | 3rd Oct, 2017, 01:36: PM

Expert Answer:

 

We see that the side of the square = 8 cm

So the diagonal of the square = begin mathsize 12px style square root of 8 squared plus 8 squared end root equals 8 square root of 2 end style cm

Since both are equilateral triangles, so they are equiangular, each of their angles is .

So the two triangles are similar.

Hence the ratio of their areas = ratio of squares of their corresponding sides.

 

Let A be the area of the equilateral triangle based on the side 8 cm.

Let A' be the area of the equilateral triangle based on the diagonal  cm.

begin mathsize 12px style So comma space fraction numerator straight A over denominator straight A apostrophe end fraction equals fraction numerator left parenthesis 8 right parenthesis squared over denominator left parenthesis 8 square root of 2 right parenthesis squared end fraction equals 1 half end style

Answered by  | 3rd Oct, 2017, 03:36: PM