Geometry Revisited #2

Geometry Level 3

In a right triangle , the lengths of the medians of the acute angles are $\sqrt{156}$ and $\sqrt{89}$ . Find the length of the hypotenuse of the triangle.

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The answer is 14.

1 solution

Rishabh Jain
Feb 15, 2016

Applying Pythagorus theorem:
In triangle $PBC$ : $\frac{c^2}{4}+a^2=x^2......(1)$ In triangle $ABQ$ : $\frac{a^2}{4}+c^2=y^2......(2)$ $(1)+(2)\Rightarrow \color{#D61F06}{\boxed{\color{#333333}{a^2+c^2=\frac{4}{5}(x^2+y^2)}}}$ In the given question $x^2\text{ and }y^2$ are $156$ and $89$ . $\large \therefore b=\sqrt{a^2+c^2}=\sqrt{\frac{4}{5}(245)}$ $\huge~~~~~~~~~~~~~~~~~~~=\boxed{\color{#007fff}{14}}$

I too have used the same method.

Niranjan Khanderia - 5 years, 3 months ago

Nice approach ! From where do you have made the diagram ??

Chirayu Bhardwaj - 5 years, 4 months ago

Free Geo (App on Play store )... There might be many good online Geometry related sites but I don't have a information about them!!

Rishabh Jain - 5 years, 4 months ago

Geometry Revisited #2

The answer is 14.

1 solution

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