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Geometry Level pending

A F = h AF= h cm

A B = x AB=x cm

D E = y DE= y cm

Area of A B F ABF is twice the area of square A B C D ABCD .

Is it true that 4 y + x = h 4y+x=h ?

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True False

Fidel Simanjuntak by Fidel Simanjuntak , 19, Indonesia

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1 solution

Fidel Simanjuntak
Sep 27, 2016

Area of A B F ABF = 2 × 2 \times area of A B C D ABCD

x h 2 = 2 x ² \frac{xh}{2} = 2x²

h = 4 x h = 4x

That means, D F = h − x DF = h - x

D F = 4 x − x = 3 x DF= 4x-x = 3x

Now, note that D E F DEF and B C E BCE are similar.

D F B C = D E E C \frac{DF}{BC} = \frac{DE}{EC}

3 x x = y x − y \frac{3x}{x} = \frac{y}{x-y}

3 ( x − y ) = y 3(x-y) = y

3 x − 3 y = y 3x - 3y = y

3 x = 4 y 3x = 4y

Adding x x in both side

4 x = 4 y + x 4x = 4y + x

h = 4 y + x h = 4y + x

It is t r u e \boxed{true}

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