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Question Number 75783 by mr W last updated on 17/Dec/19

Commented by mr W last updated on 17/Dec/19

$$findtheareamissing.$$

Answered by mr W last updated on 17/Dec/19

Commented by mr W last updated on 17/Dec/19

$$rectangle=a\times b$$$$missingarea?=A$$$$\frac{b(a+x)}{2}=4+3=7$$$$\Rightarrow b(a+x)=14...\left(i\right)$$$$\frac{b(a+y)}{2}=4+A$$$$\Rightarrow b(a+y)=8+2A...\left(ii\right)$$$$\left(i\right)+\left(ii\right):$$$$b(2a+x+y)=22+2A$$$$\frac{a-x-y}{a}=\sqrt{\frac{1}{4}}=\frac{1}{2}$$$$\Rightarrow x+y=\frac{a}{2}$$$$\Rightarrow b(2a+\frac{a}{2})=22+2A$$$$\Rightarrow \frac{5ba}{2}=22+2A$$$$ba=1+3+4+A=8+A$$$$\Rightarrow \frac{5(8+A)}{2}=22+2A$$$$\Rightarrow 40+5A=44+4A$$$$\Rightarrow A=4$$

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