Rhombus 2

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

Correct result:

S =  2400 mm2

Solution:

a=x+y 602=482+y2 y=602482=36 mm  a2=x2+482 (x+y)2=x2+482 x2+2xy+y2=x2+482 2xy+y2=482 236x=482362 x=14 mm  a=x+y=14+36=50 mm  S=av=5048=2400 mm2 a = x+y \ \\ 60^2 = 48^2 + y^2 \ \\ y= \sqrt{ 60^2 - 48^2} = 36 \ mm \ \\ \ \\ 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 = 14 \ mm \ \\ \ \\ a = x+y = 14 + 36 = 50 \ mm \ \\ \ \\ S = a v = 50 \cdot 48 = 2400 \ \text{mm}^2 \ \\



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