Given: δtsp, ts = sp = 10cm, tp = 12cm. find: three altitudes of δtsp.

The altitudes of ΔTSP is SC is 8 unit ,

PA is 5 unit ,

TB is 5 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 =

∴  PA = 5 unit

Again

TB² = TS² - BS²

TB² = 10² - 5²

Or, TB² = 100 - 25

Or, TB =

∴ TB =  5 unit

Similarly

SC² = TS² - TC²

SC² = 10² - 6²

Or, SC² = 100 - 36

Or, SC =

∴ SC = 8 unit

Hence The altitudes of ΔTSP is SC is 8 unit , PA is 5 unit , TB is 5 unit . Answer

10cm

step-by-step explanation:

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