Question

In the given figure, O is the point inside a △MNP such that ∠MOP = 90⁰ , OM = 16 cm and OP = 12 cm. If MN = 21 cm and ∠NMP = 90⁰ then
NP = ?
(a) 25 cm
(b) 29 cm
(c) 33 cm
(d) 35 cm

Answer 1

Now, In right triangle MOP
By using Pythagoras theorem, we have
$$\begin{gathered} {\mathrm{MP}}^2={\mathrm{PO}}^2+{\mathrm{OM}}^2 \\ ={12}^2+{16}^2 \\ =144+256 \\ =400 \\ \therefore {\mathrm{MP}}^2=400 \\ \Rightarrow \mathrm{MP}=20\mathrm{cm} \end{gathered}$$
Now, In right triangle MPN
By using Pythagoras theorem, we have
$$\begin{gathered} {\mathrm{PN}}^2={\mathrm{NM}}^2+{\mathrm{MP}}^2 \\ ={21}^2+{20}^2 \\ =441+400 \\ =841 \\ \therefore {\mathrm{MP}}^2=841 \\ \Rightarrow \mathrm{MP}=29\mathrm{cm} \end{gathered}$$
Hence, the correct answer is option (b).