1 answer:
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Step-by-step explanation:
1)
In a right triangle longest side is hypotenuse and the remaining two sides represent the perpendicular legs.
Hence, from the given question it is obvious that 25 is hypotenuse and 20 and 15 are perpendicular legs.
Now, by Pythagorean theorem:
2)
Because all right triangles have one hypotenuse and two perpendicular legs.
Answer:
{ 4 }
Step-by-step explanation:
First you need to solve the equation. Then you need to write the solutions as a set.
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I like to use a graphing calculator to solve equations involving roots. That helps avoid extraneous solutions. Here, the graph of the left side intersects the graph of the right side at x=4. There is exactly one solution, so the solution set is ...
{ 4 }
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Solving this algebraically, you would isolate the radical, then "undo" it by squaring both sides of the equation. Then solve the resulting quadratic. That will have 2 solutions, only one of which will work in the original equation.
√(5x +16) -2 = 3x -8 . . . . given
√(5x +16) = 3x -6 . . . . . . add 2
5x +16 = (3x -6)^2 . . . . . square both sides
5x +16 = 9x^2 -36x +36 . . . . expand the square
9x^2 -41x +20 = 0 . . . . . . subtract (5x+16) to put into standard form
Factors of 9·20 = 180 that have a sum of 41 are 5 and 36, so we can rewrite this equation as ...
9x^2 -36x -5x +20 = 0
9x(x -4) -5(x -4) = 0 . . . . . . factor by pairs
(9x -5)(x -4) = 0
The values of x that make this equation true are the values that make the factors be zero: 5/9 and 4. Trying these in the equation, we find ...
√(5(5/9) +16) -2 = 13/3 -2 = 2 1/3 . . . . value of the left side for x = 5/9
3(5/9) -8 = -6 1/3 . . . . . . value of the right side for x=5/9; not the same
x = 5/9 is NOT A SOLUTION
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√(5(4)+16) -2 = √36 -2 = 4 . . . . value of the left side for x = 4
3(4) -8 = 12 -8 = 4 . . . . . . value of the right side for x=4. These are the same, so ...
x = 4 is a solution
The set of solutions is then ...
{ 4 } . . . . . solution set
