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Question Number 67072 by TawaTawa last updated on 22/Aug/19

Answered by mr W last updated on 22/Aug/19

Commented by mr W last updated on 22/Aug/19

$$sidelength=25+15=40$$$$\frac{SQ}{AP}=\frac{QB}{AB}=\frac{2}{2+3}=\frac{2}{5}$$$$\Rightarrow SQ=\frac{2}{5}\times 25=10$$$$\Rightarrow QB=\frac{2}{2+3}\times 40=16$$$$\frac{RT}{QB-RT}=\frac{BC}{SQ}=\frac{40}{10}=4$$$$\frac{RT}{16-RT}=4$$$$5\times RT=64$$$$\Rightarrow RT=\frac{64}{5}$$$$A_{green}=\frac{1}{2}\times 40\times \frac{64}{5}=256{cm}^2$$

Commented by TawaTawa last updated on 22/Aug/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{I}\mathrm{really}\mathrm{appreciate}.$$

Commented by TawaTawa last updated on 22/Aug/19

$$\mathrm{Sir},\mathrm{please}\mathrm{i}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{understand}\mathrm{this}\mathrm{rule}:\frac{\mathrm{RT}}{\mathrm{QB}-\mathrm{RT}}=\frac{\mathrm{BC}}{\mathrm{SQ}}$$$$\mathrm{i}\mathrm{understand}\mathrm{the}\mathrm{rest}\mathrm{as}\mathrm{similar}\mathrm{triangle}.\mathrm{Thanks}\mathrm{for}\mathrm{your}\mathrm{time}\mathrm{sir}$$

Commented by mr W last updated on 22/Aug/19

Commented by mr W last updated on 22/Aug/19

$$\frac{RT}{UR}=\frac{CB}{SQ}$$$$UR=QB-RT$$$$\frac{RT}{QB-RT}=\frac{CB}{SQ}$$$$\frac{RT}{16-RT}=\frac{40}{10}=4$$$$5\times RT=64$$$$\Rightarrow RT=\frac{64}{5}$$

Commented by TawaTawa last updated on 22/Aug/19

$$\mathrm{I}\mathrm{understand}\mathrm{this}\mathrm{now}\mathrm{sir}.\mathrm{very}\mathrm{clear},\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$$$$$$$\mathrm{But}\mathrm{what}\mathrm{rule}\mathrm{is}:\frac{\mathrm{RT}}{\mathrm{UR}}=\frac{\mathrm{CB}}{\mathrm{SQ}}$$

Commented by TawaTawa last updated on 22/Aug/19

$$\mathrm{I}\mathrm{know}\mathrm{similar}\mathrm{triangle}\mathrm{but}\mathrm{i}\mathrm{dont}\mathrm{know}\mathrm{when}\mathrm{to}\mathrm{use}\mathrm{the}\mathrm{above}\mathrm{sir}$$

Commented by mr W last updated on 22/Aug/19

$$\frac{RT}{UR}=\frac{RC}{RQ}=\frac{CB}{SQ}$$

Commented by TawaTawa last updated on 22/Aug/19

$$\mathrm{I}\mathrm{appreciate}\mathrm{your}\mathrm{time}\mathrm{sir}.\mathrm{I}\mathrm{have}\mathrm{new}\mathrm{question}\mathrm{on}\mathrm{the}\mathrm{group}\mathrm{sir}.$$

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