In triangle xyz, xz = 25 cm, xy = 24 cm and yz = 7 cm. Find the inradius.
Answers
Answer:
inradius = 3 cm
Step-by-step explanation:
In triangle xyz, xz = 25 cm, xy = 24 cm and yz = 7 cm. Find the inradius.
Method 1 - Right Angle Triangle
Here we can see that
xz² = xy² + yz²
=> 25² = 24² + 7²
=> 625 = 576 + 49
=> 625 = 625
so this a right angle triangle
with base & height = xy & yz = 24 & 7 cm
hypotenuse = xz = 25 cm
The radius of an incircle of a right triangle (the inradius) = (base + height - hypotenuse)/2
inradius = (xy + yz - xz)/2
=>inradius = (24+7 -25)/2
=> inradius = 6/2
=> inradius = 3 cm
Method 2
s = (25+24+7)/2 = 28 cm
Area of Triangle using hero formula = √{(28)(28-25)(28-24)(28-7)}
=> Area of Triangle = √(28 × 3 × 4 × 21)
=> Area of Triangle = √(84 × 84)
=> area of Triangle = 84 cm²
inradius = 2 * area / (sum of Sides)
=> inradius = 2 * 84 / (25 + 24 + 7)
=> inradius = 168/56
=> Inradius = 3 cm