Hello from MrBillDoesMath!
Answer:
15
Discussion:
Given: measure angle STQ = 7x + 55. But, as shown, STQ is a right angle so
7x + 55 = 90 => subtract 55 from each side
7x = 90 -55 = 35 => divide each side by 7
x = 35/7 = 5
Since RS = (x+1) + (2x-1) where x = 5.
RS = (5 + 1) + (2*5 -1)
= 6 + 9
= 15
I don't know what choice the answer is as your diagram only shows Choice A
Thank you,
MrB
Answer:
[tex]RS=15[/tex]
Step-by-step explanation:
We have been given a triangle. We are asked to find the measure of segment RS.
Since QT is altitude of our given triangle, so angle QTR and angle QTS are right triangles.
Let us solve for x by equating measure of angle STQ with 90 degrees.
[tex]m\angle STQ=90[/tex]
[tex]7x+55=90[/tex]
[tex]7x+55-55=90-55[/tex]
[tex]7x=35[/tex]
[tex]\frac{7x}{7}=\frac{35}{7}[/tex]
[tex]x=5[/tex]
We can see that segment RS is RT plus TS.
[tex]RS=RT+TS[/tex]
[tex]RS=x+1+2x-1[/tex]
[tex]RS=x+2x[/tex]
[tex]RS=3x[/tex]
Upon substituting [tex]x=5[/tex], we will get:
[tex]RS=3*5[/tex]
[tex]RS=15[/tex]
Therefore, the length of segment RS is 15 units.
