How do I find the value of x here?

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lemjay | High School Teacher | (Level 2) Senior Educator

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To solve for x, apply similar triangles.

So, draw the triangles separately to determine the corresponding sides. (See image below.)

Then, consider triangle 1 and triangle 2.

Express in ratio the shortest leg of these two triangles.

ratio1 : `x/5`

Also, express in ratio their corresponding hypotenuse .

ratio2: `12/13`

Set the two ratios equal to each other.

`x/5=12/13`

And isolate x. To do so, multiply both sides by 5.

`x/5*5=12/13*5`

`x=60/13`

`x=4.62`

Hence, `x=4.62`  .

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