Question

A thin wire of length 18 cm is bent into the shape shown. Calculate the length from A to B

Answer 1

Step-by-step explanation:

18-(3 CM+3 CM)=12

12-3 CM=9

a^2+b^2=c^2

3 CM^2+9^2=x^2

90=x^2

sqrt 90=9.48683298051

Answer 2

The length of AB is $3\sqrt{10}$ cm.

A thin wire is bent in the shape as attached in the figure. The second picture attached shows all other construction needed to solve this.

$\triangle AEB$ forms a right-angled triangle,

So, according to Pythagoras theorem,

$AE^2+BE^2=AB^2\\\\\implies 3^2+9^2=AB^2\\\\\implies 9+81=AB^2\\\\\implies 90=AB^2\\\\\implies \sqrt{90}=AB\\ \\\implies AB=3\sqrt{10} \ cm$

Hence, $3\sqrt{10}$ cm is the required length of A to B.

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