Inscribed circle

XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.

Correct result:

S =  157.5 cm2

Solution:

r=5 y=14 s=(x+y+z)/2 x2=y2+z2 S=sr S=zy/2 zy/2=(z+y+z2+y2)/(2r)  z=2⋅ (y⋅ r−r2)/(y−2⋅ r)=2⋅ (14⋅ 5−52)/(14−2⋅ 5)=452=22.5 x=y2+z2=142+22.52=532=26.5 S=z⋅ y/2=22.5⋅ 14/2=3152=3152 cm2=157.5 cm2

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