Question

Triangle 𝑋𝑌𝑍 is right-angled at vertex 𝑍. Calculate the length of 𝑌𝑍, if 𝑋𝑌 = 13 𝑐𝑚 and 𝑋𝑍 = 12 𝑐𝑚.

Answer 1

Step: Applying Pythagoras theorem to find length of base

𝑆𝑖𝑛𝑐𝑒, ∆XYZ is right angled at vertex Z,

According to Pythagoras theorem,

$(Hypotenuse{)}^2$ = $(Perpendicular{)}^2$ + $(Base{)}^2$

$X{Y}^2$ = $X{Z}^2$ + $Y{Z}^2$

$(13{)}^2$ = $(12{)}^2$ + $(YZ{)}^2$

169 - 144 = $(YZ{)}^2$

25 = $(YZ{)}^2$

YZ = 5 cm

Hence, the length of YZ is 5 cm.