Let x represent the length of the shorter leg.
Longer leg: 5x +19
Hypotenuse: 5x +20
Pythagorean theorem:
.. x^2 +(5x +19)^2 = (5x +20)^2
.. x^2 +25x^2 +190x +19^2 = 25x^2 +200x +20^2 . . . . . . eliminate parentheses
.. x^2 -10x -39 = 0
.. (x -13)(x +3) = 0
.. x = 13 . . . . . . . . . . leg lengths must be positive
The side length of the triangle are 13, 84, 85 feet.
Given:
The given equation is:

A line is perpendicular to the given line and passes through the point (4,-1).
To find:
The equation of required line.
Solution:
The slope intercept form of a line is:

Where, m is slope and b is y-intercept.
We have,

Here, the slope of the line is -4 and the y-intercept is 3.
Let the slope of required line be m.
We know that the product of slopes of two perpendicular lines is -1. So,



The slope of required line is
and it passes through the point (4,-1). So, the equation of the line is:




Therefore, the equation of the required line is
.
The value of the 8 in Samira's number is 8,000. The value of the 8 in Tineka's number is 800.
I believe your answer would be Option D) 1000.
Hope this helps! :)
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