Hello :
<span>note :
an equation of the
circle Center at the w(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : </span><span>x²+y²-16x+6y+53=0
(</span>x²-16x) +( y²+6y ) +53 = 0
(x² -2(8)x +8² - 8²) +(y² +2(3)x -3²+3² ) +53=0
(x² -2(8)x +8²) - 8² +(y² +2(3)x +3²)-3² +53=0
(x-8)² +( y+3)² = 20
the center is : w(8,-3) and ridus : r = <span>√20</span>
Answer:
The shortest side is 3”
Step-by-step explanation:
In this question, we can observe that we have 3 sides of a triangle which are not equal in length. These sides are the long, medium and short.
We now have some mathematical statements according to the question.
Since these statements are referencing the short side, let’s start from there.
Let the length of the short side be x. The medium side is 4” more than the short side. This means that the medium side will be the short side plus 4 which mathematically is (x + 4)“. Also, we know that the longest side is 5 times the length of the shortest side. This is mathematically equal to 5x.
Lastly, we are made to know that the perimeter of the triangle is 25”. The perimeter of a triangle can be obtained by adding all the lengths together. This means that:
x + x +4 + 5x = 25
7x + 4 = 25
7x = 25 - 4
7x = 21
x = 21/7
x = 3”
