Rectangular triangles

The lengths of the corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles?
At what ratio are the areas of these triangles? A smaller rectangular triangle has legs 6 and 8 cm.

Correct answer:

p₁ =  2:5
p₂ =  4:25

Step-by-step explanation:

$$\begin{gathered} a:A=2:5 \\ a=6\text{cm} \\ b=8\text{cm} \\ r=\frac{2}{5}=0.4 \\ A=a/r=6/\frac{2}{5}=6:\frac{2}{5}=6\cdot \frac{5}{2}=\frac{6\cdot 5}{2}=\frac{30}{2}=15\text{cm} \\ B=b/r=8/\frac{2}{5}=8:\frac{2}{5}=8\cdot \frac{5}{2}=\frac{8\cdot 5}{2}=\frac{40}{2}=20\text{cm} \\ {p}_1=r=\frac{2}{5}=0.4=2:5 \end{gathered}$$

Try calculation via our triangle calculator.

$$\begin{gathered} S_1=\frac{a\cdot b}{2}=\frac{6\cdot 8}{2}=24{\text{cm}}^2 \\ {S}_2=\frac{A\cdot B}{2}=\frac{15\cdot 20}{2}=150{\text{cm}}^2 \\ {r}_2=S_1/S_2=24/150=\frac{4}{25}=0.16 \\ {p}_2=r^2={\frac{2}{5}}^2=\frac{4}{25}=0.16=4:25 \end{gathered}$$

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