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Given the triangle below, write the value of y in simplest radical form:

Given the triangle below, write the value of y in simplest radical form:-example-1
User Xaxxus
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The given problem states you have a triangle that can be divides into 2 smaller right triangles that can be used to solve the missing sides x and y.

Starting from the left triangle to the left we can use the pythagorean to solve for x

The missing side of the triangle is the hypotenuse and using the pythagorean we obtain:


\begin{gathered} a^2+b^2=c^2 \\ 9^2+5^2=x^2 \\ 81+25=x^2 \\ 106=x^2 \\ x=\sqrt[]{106} \\ \end{gathered}

Applying the same concept, solve side y using the pythagorean on the triangle to the right

In this triangle the missing side is also the hypotenuse, applying the pythagorean we obtain:


\begin{gathered} a^2+b^2=c^2 \\ 3^2+5^2=y^2 \\ 9+25=y^2 \\ 34=y^2 \\ y=\sqrt[]{34} \end{gathered}

simplify the radicals by decomposing the numbers inside the roots into primes.

none of the radicals can be simplified.

ANSWER:


x=\sqrt[]{106};y=\sqrt[]{34}

Given the triangle below, write the value of y in simplest radical form:-example-1
Given the triangle below, write the value of y in simplest radical form:-example-2
Given the triangle below, write the value of y in simplest radical form:-example-3
User Mayur Manani
by
8.0k points

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