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katrin [286]
3 years ago
11

Find the value of x on this triangle

Mathematics
1 answer:
blondinia [14]3 years ago
6 0
Look at the picture.

ΔABD and ΔBCD are similar, therefore:

\dfrac{y}{5}=\dfrac{11}{y}\ \ \ |\cross\ multiply\\\\y^2=55\to y=\sqrt{55}

Use Pythagorean theorem:

x^2=5^2+(\sqrt{55})^2\\\\x^2=25+55\\\\x^2=80\to x=\sqrt{80}\\\\x=\sqrt{16\cdot5}\\\\x=\sqrt{16}\cdot\sqrt5\\\\\boxed{x=4\sqrt5}

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