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Answers
Question :
There are four points P, Q, R and S marked on the side of the square ABCD so that each side is divided in the ratio of 3 : 2 and PQRS also forms a square. The ratio of area of PQRS and the area of ABCD is given by - 13 : 25
Answer :
Refer to attachment
Ratio of which each side of square ABCD is divided = 3 : 2
Let the parts which were divided in the ratio be 3x and 2x units
Side of the square ABCD = AP + BP = 2x + 3x = 5x units
Area of a square = Side² sq.units
Area of the square ABCD = ( 5x )² = 25x² sq.units
Consider ΔSDR
∠SDR = 90° [ Angle in a square ]
So, ΔSDR is a Right angled triangle
By Pythagoras theorem
SR² = SD² + DR²
SR² = ( 2x )² + ( 3x )²
SR² = 4x² + 9x²
SR² = 13x²
SR √13 x units
i.e Side of the square PQRS ( SR ) = √13 x units
Area of a square = Side² sq.units
Area of the square PQRS = ( √13 x )² = 13x² sq.units
Ratio of area of square PQRS and the area of the square ABCD = 13x² sq. units / 25x² sq.units
= 13 / 25
= 13 : 25
Hence the ratio of area of square PQRS and area of ABCD is 13 : 25.
Answer:
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