Question

In isosceles triangle abc right angled at b prove that ac2=2ab2

Answer 1

$\textbf{Given:}$

$\textsf{ABC is a isoceles triangle at B}$

$\textbf{To prove:}$

$\mathsf{AC^2=2\;AB^2}$

$\textbf{Solution:}$

$\textsf{Since ABC is an isoceles right angled triangle,}$

$\mathsf{we\;have\;AB=BC}$

$\mathsf{In\;right\;triangle\;ABC\;,by\;pythagoras\;theorem}$

$\mathsf{AC^2=AB^2+BC^2}$

$\mathsf{AC^2=AB^2+AB^2}$$\mathsf{\;\;\;(\because\;\;AB=BC\;\;\;)}$

$\implies\boxed{\mathsf{AC^2=2\;AB^2}}$

$\textbf{Find more:}$

The square of the hypotenuse of a right angled isosceles triangle is 288 cm find the length of the legs

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