Diagonals of a rhombus 2

One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm², find the side of the rhombus.

Correct answer:

a =  10 cm

Step-by-step explanation:

$$\begin{gathered} u=4+v=4+12=16 \\ S=96{\text{cm}}^2 \\ S={\displaystyle \frac{uv}{2}}={\displaystyle \frac{(4+v)v}{2}} \\ 96=(4+v)\ast v\mathrm{/}2 \\ 96=(4+v)\cdot v\mathrm{/}2 \\ -0.5v^2-2v+96=0 \\ 0.5v^2+2v-96=0 \\ a=0.5;b=2;c=-96 \\ D=b^2-4ac=2^2-4\cdot 0.5\cdot (-96)=196 \\ D>0 \\ {v}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{-2\pm \sqrt{196}}{1}}=-2\pm 14\sqrt{1} \\ {v}_{1,2}=-2\pm 14 \\ {v}_1=12 \\ {v}_2=-16 \\ \text{ Factored form of the equation: } \\ 0.5(v-12)(v+16)=0 \\ v=v_1=12\text{ cm } \\ u=4+v=4+12=16\text{ cm } \\ a=\sqrt{(u\mathrm{/}2{)}^2+(v\mathrm{/}2{)}^2}=\sqrt{(16\mathrm{/}2{)}^2+(12\mathrm{/}2{)}^2}=10\text{ cm} \end{gathered}$$

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