Question Number 186322 by Rupesh123 last updated on 03/Feb/23
Answered by mr W last updated on 04/Feb/23
Commented by mr W last updated on 04/Feb/23
![(2+a)^2 +(2+2+a)^2 =(a+2+a)^2 a^2 −2a−8=0 (a−4)(a+2)=0 ⇒a=4 [ABC]=((6×8)/2)=24 ✓](https://www.tinkutara.com/question/Q186372.png)
$$\left(\mathrm{2}+{a}\right)^{\mathrm{2}} +\left(\mathrm{2}+\mathrm{2}+{a}\right)^{\mathrm{2}} =\left({a}+\mathrm{2}+{a}\right)^{\mathrm{2}} \\ $$$${a}^{\mathrm{2}} −\mathrm{2}{a}−\mathrm{8}=\mathrm{0} \\ $$$$\left({a}−\mathrm{4}\right)\left({a}+\mathrm{2}\right)=\mathrm{0} \\ $$$$\Rightarrow{a}=\mathrm{4} \\ $$$$\left[{ABC}\right]=\frac{\mathrm{6}×\mathrm{8}}{\mathrm{2}}=\mathrm{24}\:\checkmark \\ $$