Rhombus 2

Calculate the rhombus area, which has a height v=48 mm and shorter diagonal u = 60 mm long.

Correct answer:

S =  2400 mm²

Step-by-step explanation:

$$\begin{gathered} a=x+y \\ 60^2=48^2+y^2 \\ y=\sqrt{60^2-48^2}=36mm \\ {a}^2=x^2+48^2 \\ (x+y{)}^2=x^2+48^2 \\ {x}^2+2xy+y^2=x^2+48^2 \\ 2xy+y^2=48^2 \\ 2\cdot 36\cdot x=48^2-36^2 \\ x=14mm \\ a=x+y=14+36=50mm \\ S=av=50\cdot 48=2400{\text{mm}}^2 \end{gathered}$$

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