Question

911 + 18 16. Equilateral triangles P, Q, R and S are such that the altitude of triangle P is the side of triangle Q, the altitude of triangle Q is the side of triangle R and the altitude of triangle R is the side of the triangle S. If the area of triangle P is 2 cm? then the area of triangle S (in cm2) is 15 27​

Answer 1

Answer:

△ABC is an Equilateral triangle such that,

AB=BC=AC

Construction:

Draw an Altitude AE such that,

 E lies on BC and

AE perpendicular to BC

In △AEB

By Pythagoras Theorem,

AB2=AE2+EB2 (1)

In △AED

By Pythagoras Theorem,

AD2=AE2+ED2 (2)

From 1) and 2)

AD2=ED2+AB2−EB2 (3)

Since, EB=21BC=2AB=63AB and

ED=6BC=6AB

∴ AD2=36AB2+AB2−369AB2

∴ 9AD2=7AB2

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