Pythagorean 81883

Hello, I have a problem calculating the height on side z in the general triangle XYZ, where z=4 cm, x=1.5 cm, and y=3.7 cm. It was assigned in 8th grade when discussing the Pythagorean theorem. Thank you.

Correct answer:

v =  1.3875 cm

Step-by-step explanation:

$$\begin{gathered} z=4\text{cm} \\ x=1.5\text{cm} \\ y=3.7\text{cm} \\ z>y>x \\ test:z^2=x^2+y^2 \\ {t}_1=z^2=4^2=16 \\ {t}_2=x^2+y^2=1.5^2+3.7^2=\frac{797}{50}=15.94 \\ {t}_1=t_2 \\ \sphericalangle \angle XZY=90{}^{\circ } \\ S=\frac{x\cdot y}{2}=\frac{1.5\cdot 3.7}{2}=\frac{111}{40}=2.775{\text{cm}}^2 \\ S=\frac{z\cdot v}{2} \\ v=\frac{2\cdot S}{z}=\frac{2\cdot 2.775}{4}=1.3875\text{cm} \end{gathered}$$

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