Right-angled 80745

The area of a right-angled triangle KLM with a right angle at the vertex L is 60 mm square, and its hypotenuse k is 10 mm long. Triangles KLM and RST are similar. The similarity ratio is k=2.5. Calculate the area of triangle RST.

Correct answer:

S₂ =  9.6 mm²

Step-by-step explanation:

$$\begin{gathered} S_1=60{\text{mm}}^2 \\ k=10\text{mm} \\ {S}_1=\frac{k\cdot m}{2} \\ m=2\cdot S_1/k=2\cdot 60/10=12\text{mm} \\ w=2.5 \\ k:r=w \\ l:s=w \\ m:t=w \\ r=k/w=10/2.5=4\text{mm} \\ t=m/w=12/2.5=\frac{24}{5}=4.8\text{mm} \\ {S}_2=\frac{r\cdot t}{2}=\frac{4\cdot 4.8}{2}=\frac{48}{5}=9.6=9.6{\text{mm}}^2 \\ \text{ Verifying Solution: } \\ {S}_3=S_1/w^2=60/2.5^2=\frac{48}{5}=9.6{\text{m}}^2 \end{gathered}$$

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