Answer:
TS is 1
Step-by-step explanation:
The given parameters are;
ΔMNP is similar to ΔTSR
[tex]\overline {NQ}[/tex] and [tex]\overline {SU}[/tex] are angle bisectors of ∠MNP and ∠TSR respectively
MN = 2, TS = n + 2, NP = 3, SU = 1, NQ = n + 3
We have;
MN and TS are corresponding sides
[tex]\overline {NQ}[/tex] and [tex]\overline {SU}[/tex] are corresponding sides
Therefore, we have;
MN/TS = [tex]\overline {NQ}[/tex]/[tex]\overline {SU}[/tex] which gives;
2/(n + 2) = (n + 3)/1
(n + 2)·(n + 3) = 2
n² + 3·n + 2·n + 6 = 2
∴ n² + 5·n + 4 = 0, which gives, by factorization;
(n + 1)·(n + 4) = 0
∴ n - 1 or n = -4
TS = n + 2
When n = -1 TS = -1 + 2 = 1
When n = -4, TS = -4 + 1 = -3
Therefore, for a natural number value, we have, n = -1 and TS = 1.
