Question

In the given figure o l is 3 cm is 5 cm or m is unknown if P is 90 degree find PM

Answer 1

From the figure, we observe that

∠LOP = ∠MOP ,

OL = 3cm , OP = 5cm ,

∠PLO = ∠PMO [ as right angles ]

Let us prove that ΔLOP ≅Δ MOP

From ΔLOP and Δ MOP we note that

∠LOP = ∠MOP

OP = OP [common]

∠PLO = ∠PMO [ right angles ]

Hence , ΔLOP ≅ΔMOP

PM = PL [ by CPCT ]—-(i)

By Pythagoras theorem we can determine the value of PL

In ΔPLO ,

OP²= LP²+OL²

[5]²= [3]²+LP²
25= 9 +LP²

LP²= 25- 9

LP= √16 = 4cm

As from above equation (i) we know that PM= PL

So , PL = PM = 4cm.



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