Question-89097

Question Number 89097 by TawaTawa1 last updated on 15/Apr/20

Commented by mr W last updated on 15/Apr/20

\sqrt{5^{2} + {(10 + 5)}^{2}} = 5 \sqrt{10}

s = 5 \sqrt{10} - \frac{5}{5 \sqrt{10}} (15 + 5) = 3 \sqrt{10}

a r e a = s^{2} = 9 \times 10 = 90

Answered by $@ty@m123 last updated on 15/Apr/20

L e t s i d e s o f t h e r i g h t a n g l e d △ w i t h

h y p o t a n e o u s 5 b e

x a n d y w h e r e y > x . T h e n

x^{2} + y^{2} = 5^{2} \dots (1)

L e t z b e t h e s i d e o f c o l o u r e d s q u a r e .

T h e n,

\frac{x}{y} = \frac{y}{y + z} = \frac{5}{15}

\frac{x}{y} = \frac{y}{y + z} = \frac{1}{3}

\Rightarrow 3 y = y + z \Rightarrow 2 y = z \dots (2)

& y = 3 x \dots . . (3)

F r o m (1) & (3),

{(\frac{y}{3})}^{2} + y^{2} = 25

\frac{y^{2}}{9} + y^{2} = 25

10 y^{2} = 25 \times 9

y^{2} = \frac{45}{2} \dots (4)

∴ F r o m (2),

z^{2} = 4 y^{2}

\Rightarrow A r e a o f c o l o u r e d s q u a r e = 4 \times \frac{45}{2}

= 90 s q . u n i t

Commented by john santu last updated on 15/Apr/20

s o m e t h i n g w r o n g s i r

i t s h o u l d b e \frac{x}{y} = \frac{5}{15} = \frac{1}{3}

y = 3 x \Rightarrow x^{2} + y^{2} = 10 x^{2} = 25

x^{2} = \frac{5}{2} \Rightarrow z = 6 x

\Rightarrow z^{2} = 36 x^{2} = 36 \times \frac{5}{2} = 90 s q u n i t

Commented by $@ty@m123 last updated on 15/Apr/20

T h a n k s f o r c o r r e c t i o n .

I a m e x p e r t i n c o m m i t t i n g s i l l y m i s t a k e s .

:) :) :)

Commented by john santu last updated on 15/Apr/20

⋮) ⋮) h a h a h a