# Sides of some triangles are given below.

Question.

Sides of some triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.

(i) 7 cm, 24 cm, 25 cm

(ii) 3 cm, 8 cm, 6 cm

(iii) 50 cm, 80 cm, 100 cm

(iv) 13 cm, 12 cm, 5 cm

Solution:

(i) $(7)^{2}+(24)^{2}=49+576=625=(25)^{2}$

Therefore, given sides $7 \mathrm{~cm}, 24 \mathrm{~cm}, 25 \mathrm{~cm}$ make a right triangle.

(ii) $(6)^{2}+(3)^{2}=36+9=45$

$(8)^{2}=64$

$(6)^{2}+(3)^{2} \neq(8)^{2}$

Therefore, given sides $3 \mathrm{~cm}, 8 \mathrm{~cm}, 6 \mathrm{~cm}$ does not make a right triangle.

(iii) $(50)^{2}+(80)^{2}=2500+6400=8900$

$(100)^{2}=10000$

$(50)^{2}+(80)^{2} \neq 100^{2}$

Therefore, given sides $50 \mathrm{~cm}, 80 \mathrm{~cm}, 100 \mathrm{~cm}$ does not make a right triangle.

(iv) $(12)^{2}+(5)^{2}=144+25=169=(13)^{2}$

Therefore, given sides $13 \mathrm{~cm}, 12 \mathrm{~cm}, 5 \mathrm{~cm}$ make a right triangle.