Question-218844

Question Number 218844 by Spillover last updated on 16/Apr/25

Answered by som(math1967) last updated on 16/Apr/25

let lenth of rectangle=l,width=b 2l+6b=4l+2b=side of square ⇒4b=2l⇒l=2b l×b=18⇒2b^2 =18⇒b=3,l=6 side of square=2×6+6×3=30cm area of square=900cm^2 area 24 rectangles=24×18=432cm^2 blue area=900−432=468cm^2

$${let}\:{lenth}\:{of}\:{rectangle}={l},{width}={b} \\ $$$$\:\mathrm{2}{l}+\mathrm{6}{b}=\mathrm{4}{l}+\mathrm{2}{b}={side}\:{of}\:{square} \\ $$$$\Rightarrow\mathrm{4}{b}=\mathrm{2}{l}\Rightarrow{l}=\mathrm{2}{b} \\ $$$$\:{l}×{b}=\mathrm{18}\Rightarrow\mathrm{2}{b}^{\mathrm{2}} =\mathrm{18}\Rightarrow{b}=\mathrm{3},{l}=\mathrm{6} \\ $$$$\:{side}\:{of}\:{square}=\mathrm{2}×\mathrm{6}+\mathrm{6}×\mathrm{3}=\mathrm{30}{cm} \\ $$$${area}\:{of}\:{square}=\mathrm{900}{cm}^{\mathrm{2}} \\ $$$${area}\:\mathrm{24}\:{rectangles}=\mathrm{24}×\mathrm{18}=\mathrm{432}{cm}^{\mathrm{2}} \\ $$$$\:{blue}\:{area}=\mathrm{900}−\mathrm{432}=\mathrm{468}{cm}^{\mathrm{2}} \\ $$

Answered by Spillover last updated on 16/Apr/25