The sum of the three numbers is 69. if the second number is equal to the first diminished by 8, and the third number is 5 times the first. what is the numbers? if x represents the first number, then which of the following equations could be used to solve the problem?

The side x is an hypotenuse side to one of the right triangles formed by

altitude of the given triangle that has solid lines.

x is approximately 31.812

Reasons:

The figure shows a triangle with an altitude that forms two triangles inside

the main triangle.

By Pythagoras's theorem, we have;

For the right triangle on the left;

22² = h² + 16²

h² = 22² - 16² = 228

h² = 228

h = √228 = 2·√57

h = 2·√57

In the right triangle to the right, we have;

The length of the top base, b = 44 - 16 = 28

The square of the hypotenuse, x² = h² + b²

∴ x² = 228 + 28² = 1012

x = √(1012) = 2·√253

x = 2·√253 ≈ 31.812

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