# BDEF IS A SQUARE INSCRIBED IN AN ISOSCELES RIGHT TRIANGLE PBQ RIGHT ANGLED AT B. IF PF=ED, FIND RATIO OF ar (BDEF) and ar (EDQ). PLS EXPLAIN.

2
by annat1bhava

## Answers

2016-03-08T18:49:33+05:30
PF = ED = FB -----[As it is A Right Isosceles Triangle]
So,
F is the midpoint Of PB And Also PB = BQ
Let BD = x
BD = DE = DQ = x

Area Of BDEF = x²
Area Of EDQ = 1/2 x² = x²/2
Ratio Of These Two = x² / (x²/2)
Area Of BDEF/Area Of EDQ  = 2 : 1

Hope U Understood
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Thankx
2016-03-08T18:54:50+05:30
PF = ED and ED = BF (opposite sides of a square )
i.e. PE = BF
so,
F is the midpoint & EF II DB OR EF LL QB ( square is also a parallelogram)
so,
E is the midpoint of PQ
now,
E is the midpoint of PQ and ED II BF or ED II BP

i.e. D is the midpoint of QB

so,

QD = DB and DB = DE (sides of a square)

Now let QD = X

Therefore, QD = DB = ED = X

Area of triangle EDQ = ½*ED * QD = a²/2

Area of the square BDEF = DB * ED = a²

Therefore their ratio is = a² / a² / 2

= 2 /1

= 2:1

I hope it helps……………..