Question

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

Answer 1

Answer:

Case 1

12 and 13 are legs, then find the hypotenuse.

• c = $\sqrt{12^2+13^2} = \sqrt{313}$ ≈ 17.69

Case 2

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

• b = $\sqrt{13^2-12^2} = \sqrt{25} = 5$

Answer 2

Answer:

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=$\sqrt{13²-12²}=\sqrt{25}=5$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=$\sqrt{13²-12²}=\sqrt{25}=\bold{\large{5}}$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=$\sqrt{13²+12²}=\sqrt{313}=\bold{\large{17.7}}$units