Question

In a right triangle, two sides are 12 and 13. Find the measure of the third side. Consider all cases

Answer 1

Solution given:

Case 1:

if base=12

hypotenuse=13

perpendicular=??

By using Pythagoras law

hypotenuse²=perpendicular²+base²

13²=perpendicular ²+12²

perpendicular ²=13²-12²

perpendicular=
`√(13²-12²)=√(25)=5`units

Case:2:

Case 1:

if base=12

hypotenuse=13

perpendicular=??

By using Pythagoras law

hypotenuse²=perpendicular²+base²

13²=perpendicular ²+12²

perpendicular ²=13²-12²

perpendicular=
`√(13²-12²)=√(25)=\bold{\large{5}}`units

Case:2:

if base=12

hypotenuse=??

perpendicular=13

By using Pythagoras law

hypotenuse²=perpendicular²+base²

hypotenuse²=13 ²+12²

hypotenuse² ²=13²+12²

hypotenuse²=
`√(13²+12²)=√(313)=\bold{\large{17.7}}`units

Answer 2

Case 1

12 and 13 are legs, then find the hypotenuse.

• c =
  `√(12^2+13^2) = √(313)` ≈ 17.69

Case 2

13 is hypotenuse, 12 is a leg, find the missing leg.

• b =
  `√(13^2-12^2) = √(25) = 5`