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Question Number 215598 by Ismoiljon_008 last updated on 11/Jan/25

Commented by Ismoiljon_008 last updated on 11/Jan/25

help, please

$$\:\:\:{help},\:{please} \\ $$

Answered by mr W last updated on 12/Jan/25

Commented by mr W last updated on 11/Jan/25

((a×a)/2)=25 ⇒ a^2 =50 ((b×b)/2)=((ab)/2)+84 ⇒ ((a^2 b^2 )/(2a^2 ))=((ab)/2)+84 let X=((ab)/2)=unknown area (X^2 /(25))=X+84 X^2 −25X−25×84=0 ⇒X=((25+95)/2)=((120)/2)=60 ✓

$$\frac{{a}×{a}}{\mathrm{2}}=\mathrm{25}\:\Rightarrow\:{a}^{\mathrm{2}} =\mathrm{50} \\ $$$$\frac{{b}×{b}}{\mathrm{2}}=\frac{{ab}}{\mathrm{2}}+\mathrm{84}\:\Rightarrow\:\frac{{a}^{\mathrm{2}} {b}^{\mathrm{2}} }{\mathrm{2}{a}^{\mathrm{2}} }=\frac{{ab}}{\mathrm{2}}+\mathrm{84} \\ $$$${let}\:{X}=\frac{{ab}}{\mathrm{2}}={unknown}\:{area} \\ $$$$\frac{{X}^{\mathrm{2}} }{\mathrm{25}}={X}+\mathrm{84} \\ $$$${X}^{\mathrm{2}} −\mathrm{25}{X}−\mathrm{25}×\mathrm{84}=\mathrm{0} \\ $$$$\Rightarrow{X}=\frac{\mathrm{25}+\mathrm{95}}{\mathrm{2}}=\frac{\mathrm{120}}{\mathrm{2}}=\mathrm{60}\:\checkmark \\ $$

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