Question

prove that the area of an equilateral triangle described on the side of a square is equal to half the area of the equilateral triangle. describe on one of its diagonal

Answer 1

we first make a square of length let a units then by applying Pythagoras theorem length of diagonal will be√(a^2)+(a^2)=√2a^2=√2.a
now area of the equilateral triangle described on side length of square will be √3×(a)^2/4 and of equilateral triangle form on diagonal will be √3×(√2a)^2/4
on finding area when u divide area of eui triangle on side/diagonal u will find ratio as 1/2 whic implies that the area of equilateral triangle described on side is of half of the equilateral triangle described on its diagonal.
hope u find it help ful, if yes then mark it brianliest.:D:):-)