Answer:
The altitudes of ΔTSP is SC is 8 unit ,
PA is 5[tex]\sqrt{3}[/tex] unit ,
TB is 5[tex]\sqrt{3}[/tex] unit .
Step-by-step explanation:
Given as :
The Triangle Δ TSP having side TS , SP , TP
The measure of TS = 12 cm
The measure of SP = 10 cm
The measure of TP = 10 cm
Let The altitude from point T on side PS = TB
The altitude from point S on side PT = SC
The altitude from point P on side TS = PA
The altitude divide the sides
TS = TA + AS
PS = PB + PS
PT = PC + CT
So, From Pythagoras theorem
PA² = PS² - AS²
PA² = 10² - 5²
Or, PA² = 100 - 25
Or, PA = [tex]\sqrt{75}[/tex]
∴ PA = 5[tex]\sqrt{3}[/tex] unit
Again
TB² = TS² - BS²
TB² = 10² - 5²
Or, TB² = 100 - 25
Or, TB = [tex]\sqrt{75}[/tex]
∴ TB = 5[tex]\sqrt{3}[/tex] unit
Similarly
SC² = TS² - TC²
SC² = 10² - 6²
Or, SC² = 100 - 36
Or, SC = [tex]\sqrt{64}[/tex]
∴ SC = 8 unit
Hence The altitudes of ΔTSP is SC is 8 unit , PA is 5[tex]\sqrt{3}[/tex] unit , TB is 5[tex]\sqrt{3}[/tex] unit . Answer
