A square playground has a perimeter of 120 yards. what is the length of a diagonal of the playground?
2 answers:
Answer:
The length of the diagonal of the playground is approximately 42.42 yards.
Step-by-step explanation:
As the playground is square we know the formula for its perimeter: , where
stands for the length of the side of the playground. By the statement of the problem we know that
, then it is not difficult to find that
yards.
If we trace the diagonal we see that a right triangle is formed, where the diagonal is its hypotenuse, and its sides are the sides of the playground. Then, using Pythagoras theorem (we denote by the length of the diagonal), we have
.
Thus, the diagonal has (approximately) 42.42 yards.
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Answer:
x=−8
y=6=
Step-by-step explanation:
3x+4y=0
5x−3y=−58
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
3x+4y=0,5x−3y=−58
To make 3x and 5x equal, multiply all terms on each side of the first equation by 5 and all terms on each side of the second by 3.
5×3x+5×4y=0,3×5x+3(−3)y=3(−58)
Simplify.
15x+20y=0,15x−9y=−174
Subtract 15x−9y=−174 from 15x+20y=0 by subtracting like terms on each side of the equal sign.
15x−15x+20y+9y=174
Add 15x to −15x. Terms 15x and −15x cancel out, leaving an equation with only one variable that can be solved.
20y+9y=174
Add 20y to 9y.
29y=174
Divide both sides by 29.
y=6
Substitute 6 for y in 5x−3y=−58. Because the resulting equation contains only one variable, you can solve for x directly.
5x−3×6=−58
Multiply −3 times 6.
5x−18=−58
Add 18 to both sides of the equation.
5x=−40
Divide both sides by 5.
x=−8
The system is now solved.
x=−8,y=6
Coordinates are: (-8,6)
Graph:
