Pythagoras Theorem?

Geometry Level 3

$ABC$ is a right angled triangle with $\angle B=90^\circ$ . $M$ is the midpoint of $AC$ and $BM=\sqrt{117}$ . Sum of the lengths of the other two sides $AB$ and $BC$ is 30. Find the area of the triangle $ABC$ .

The answer is 108.

1 solution

Swapnil Das
Jun 7, 2016

Statement : In a triangle right angled at B , with M being its hypotenuse's midpoint, $AM=BM=MC$ .

As $AB+BC=30$ , ${ \left( AB \right) }^{ 2 }+{ \left( BC \right) }^{ 2 }+2\left( AB \right) \left( BC \right) =900$

$\implies$ ${ \left( AC \right) }^{ 2 }+2\left( AB \right) \left( BC \right) =900$

or, $\left( AB \right) \left( BC \right) =900-468=432$

$\implies$ $\frac { 1 }{ 2 } \left( AB \right) \left( BC \right) =\frac { 432 }{ 4 } =108.$

$\therefore$ The area of the triangle is $108$ $\text{units}$ .

good one!! @Swapnil Das

Ayush G Rai - 5 years ago

Pythagoras Theorem?

The answer is 108.

1 solution

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