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Question Number 206060 by cortano21 last updated on 06/Apr/24

Answered by mr W last updated on 06/Apr/24

Commented by mr W last updated on 06/Apr/24

$$S=areaofparallelogram$$$$S=20+22+16+X$$$$22+X-A=\frac{S}{2}=\frac{20+22+16+X}{2}$$$$\Rightarrow X-2A=14...\left(i\right)$$$$$$$$\frac{B}{A}=\frac{\mid BD\mid }{\mid AC\mid }=\frac{16}{20}=\frac{4}{5}\Rightarrow B=\frac{4A}{5}$$$$$$$$20+A+22-B=\frac{S}{2}$$$$20+A+22-\frac{4A}{5}=\frac{20+22+16+X}{2}$$$$\Rightarrow 5X-2A=130...\left(ii\right)$$$$\left(ii\right)-\left(i\right):$$$$4X=130-14$$$$\Rightarrow X=29✓$$

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