Triangles with the same shape but different size are proportional. Proportional means that their side lengths form equal ratios. To solve for x, set up a proportion.

The ratios we will create will be $\frac{long}{short} =\frac{long}{short}$ where each long and short are corresponding sides from each triangle.

So write:

$\frac{4}{x} =\frac{3}{2.25}$

To solve, cross multiply numerator with denominator.

4(2.25) = 3(x)

9 = 3x

3 =x

5 0

3 years ago

Find the hypotenuse of an isosceles right triangle when the legs each measure 3\sqrt{x} 2inches.

Tresset [83]

The hypotenuse of the right triangle measures 3 units.

<h3>How to find the hypotenuse?</h3>

Here we know that both legs measure:

$L =\frac{3}{\sqrt{2} }$

If we use the Pythagorean theorem, we will see that the hypotenuse H can be written as:

$H^2 = (\frac{3}{\sqrt{2} } )^2 + (\frac{3}{\sqrt{2} } )^2 \\\\H^2 = \frac{9}{2} + \frac{9}{2} = \frac{18}{2} = 9\\\\H = \sqrt{9} = 3$

Then we conclude that the hypotenuse of the right triangle measures 9 units.

If you want to learn more about right triangles:

brainly.com/question/2217700

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6 0

1 year ago