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Question Number 156508 by cortano last updated on 12/Oct/21

Answered by JDamian last updated on 12/Oct/21

$$\frac{A_{triangle}}{A_{\mathit{r}\mathit{e}\mathit{c}\mathit{t}\mathit{a}\mathit{n}\mathit{g}\mathit{l}\mathit{e}}}?$$$$A_{triangle}=\sqrt{s(s-a)(s-b)(s-c)}$$$$a=6+7=13$$$$b=7+8=15$$$$c=6+8=14$$$$s=\frac{a+b+c}{2}=\frac{42}{2}=21$$$$A_{triangle}=\sqrt{21(21-13)(21-15)(21-14)}=$$$$=\sqrt{21\times 8\times 6\times 7}=84$$$$A_{\mathit{r}\mathit{e}\mathit{c}\mathit{t}\mathit{a}\mathit{n}\mathit{g}\mathit{l}\mathit{e}}=width\times height=$$$$=28\times (7+8+h_{triangle})$$$$A_{triangle}=\frac{14\times h_{triangle}}{2}=84$$$$h_{triangle}=\frac{2\times 84}{14}=12$$$$A_{\mathit{r}\mathit{e}\mathit{c}\mathit{t}\mathit{a}\mathit{n}\mathit{g}\mathit{l}\mathit{e}}=28\times (7+8+12)=28\times 27$$$$\frac{A_{triangle}}{A_{\mathit{r}\mathit{e}\mathit{c}\mathit{t}\mathit{a}\mathit{n}\mathit{g}\mathit{l}\mathit{e}}}=\frac{84}{28\times 27}=\frac{1}{9}$$

Commented by cortano last updated on 12/Oct/21

$$\mathrm{wrong}.\mathrm{it}\frac{84}{756}=\frac{1}{9}$$

Commented by JDamian last updated on 12/Oct/21

is it not a square? Oops, I see now it is not a square.

Commented by Tawa11 last updated on 12/Oct/21

$$\mathrm{great}\mathrm{sir}.$$

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