Inscribed circle

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

Correct answer:

S =  157.5 cm2

Step-by-step explanation:

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 rr2)/(y2 r)=2 (14 552)/(142 5)=245=22.5 x=y2+z2=142+22.52=253=26.5 S=z y/2=22.5 14/2=157.5 cm2

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