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
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.
(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.