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Question
ABCD is a square an equilateral triangle is made on diagonal AC of this square. If height of equilateral triangle is 9 cm, then find area of square ABCD?
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Answer
for triangle:
let side be x, then half of other side is x/2, and height =9. so pythagoras 9^2+(x/2)^2=x^2
so x^2=108
for square
let side be y, applying pythagoras
diagonal(x)^2=y^2+y^2
so, 108=2y^2
y^2=54= area of square.
thanks
