Question

1. On the square ABCD. point Elies on the side AD and Flies on BC so that
BE = EF= FD = 30 cm. The area of the square (in square cms) is
A. 300
B. 900
C. 810
D. None of these​

Answer 1

Answer:

810

Step-by-step explanation:

x^2+(3x)^2=300

x=3root10

x=810

area=810

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Answer 2

According the question, here we draw a  the square ABCD,

point E lies on the side AD,  and point F lies on the side BC.      ( given)

BE = EF= FD = 30 cm...           ( given)

Let consider the side of square ABCD is p

Here we find that 3 segments cut the square ABCD into 3 horizontal parts.

where :-

DC = p =AB

DE = BF = 2p/3

CF = AE = p/3

let consider Δ DCF,

DF = 30

DC = p

CF = p/3

∴DF² = CF² + DC²

( 30)² = (p )² + ( p/3)²

900 = p² + p²/3² = p² + p²/9= 10p²/9

10p² = 900 × 9=$8100$

p² =810

Hence area of the square ABCD = 810 square unit

Ans:- Correct answer will be option-C. 810