Question

Find the area in cm2 of a rhombus whose side length is 29 cm and

whose diagonals differ in length by 2 cm

Answer 1

`\left((d)/(2)\right)^2+\left((d+2)/(2)\right)^2=29^2\\\\(d^2)/(4)+(d^2+4d+4)/(4)=841\ \ \ \ /\cdot4\\\\d^2+d^2+4d+4=3364\\\\2d^2+4d+4-3364=0\\\\2d^2+4d-3360=0\ \ \ \ /:2\\\\d^2+2d-1680=0`


`a=1;\ b=2;\ c=-1680\\\\\Delta=b^2-4ac\to\Delta=2^2-4\cdot1\cdot(-1680)=4+6720=6724\\\\\sqrt\Delta=√(6724)=82\\\\d_1=(-b-\sqrt\Delta)/(2a)\to d_1=(-2-82)/(2\cdot1) < 0\\\\d_2=(-b+\sqrt\Delta)/(2a)\to d_2=(-2+82)/(2\cdot1)=(80)/(2)=40\ (cm)\\\\d=40cm;\ d+2=42cm\\\\A_r=(d(d+2))/(2)\to A_r=(40\cdot42)/(2)=840\ (cm^2)`