Question

Solve for x and set up the proportion

Answer 1

• x/5 = 20/x
• x = 10

Explanation:

Given the altitude of a right triangle divides its hypotenuse into segments of lengths 15 and 5, you want to know the proportion and the value of x, where x is the short side of the largest triangle.

Proportion

The triangles are all similar, so the ratio of hypotenuse to short side is the same for all:

`(x)/(5)=(5+15)/(x)\\\\\boxed{(x)/(5)=(20)/(x)}`

Solution

The solution can be found by multiplying this by 5x to get ...

x² = 100

x = 10 . . . . . . . . take the square root

The value of x is 10.

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