Question 23:
x = 4
DE = 44
Question 24:
x = 25
SE = 28
Step-by-step explanation:
As RS is the perpendicular bisector of DE, it will divide DE in two equal parts DS and SE
Question number 23:
Given
DS = 3x+10
SE = 6x-2
As the two segments are equal:
[tex]DS = SE\\3x+10 = 6x-2[/tex]
Subtracting 10 from both sides
[tex]3x+10-10 = 6x-2-10\\3x = 6x-12[/tex]
subtracting 6x from both sides
[tex]3x -6x = 6x-6x-12\\-3x = -12[/tex]
Dividing both sides by -3
[tex]\frac{-3x}{-3} = \frac{-12}{-3}\\x = 4[/tex]
Now
[tex]DS = 3x+10\\= 3(4)+10\\= 12+10\\=22[/tex]
And
[tex]SE = 6x-2\\= 6(4)-2\\= 24 - 2\\=22\\DE = DS+SE\\= 22+22\\=44[/tex]
Question No 24:
Given
DS = x+3
DE = 56
We know that:
[tex]DS = \frac{1}{2}DE\\x+3 = \frac{56}{2}\\x + 3 = 28\\x = 28-3\\x = 25[/tex]
So
DS = [tex]25+3 = 28[/tex]
As DS is 28, SE will also be 28
Hence,
Question 23:
x = 4
DE = 44
Question 24:
x = 25
SE = 28
Keywords: Bisector, Line segment
Learn more about line segments at:
- brainly.com/question/629998
- brainly.com/question/6208262
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