Rhombus

The rhombus with area 95 has one diagonal that is longer by 7 than the second one. Calculate the length of the diagonals and rhombus sides.

Final Answer:

u1 =  10.72
u2 =  17.72
a =  10.36

Step-by-step explanation:

S=95 u2​ = u1​+7  S = 2u1​ u2​​ 2S = u1​⋅ (u1​+7) u12​+7 u1​ − 2 ⋅  95 = 0 x2+7x−2⋅ 95=0  x2+7 x−2⋅ 95=0 x2+7x−190=0  a=1;b=7;c=−190 D=b2−4ac=72−4⋅1⋅(−190)=809 D>0  x1,2​=2a−b±D​​=2−7±809​​ x1,2​=−3.5±14.221463 x1​=10.721462653 x2​=−17.721462653  u>0 u1​=x1​=10.7215=10.72

Our quadratic equation calculator calculates it.

u2​=u1​+7=10.7215+7=17.72
a2 = (u1​/2)2+(u2​/2)2 a=(u1​/2)2+(u2​/2)2​=(10.7215/2)2+(17.7215/2)2​=10.36

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