Rectangle diagonals

It is given a rectangle with an area of 24 cm² and a circumference of 20 cm. The length of one side is 2 cm larger than the length of the second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.

Correct answer:

u =  7.2111 cm

Step-by-step explanation:

$$\begin{gathered} S=24{\text{cm}}^2 \\ o=20\text{cm} \\ S=ab \\ o=2(a+b) \\ b=10-a \\ 24=a\cdot (10-a) \\ 24=a\cdot (10-a) \\ {a}^2-10a+24=0 \\ p=1;q=-10;r=24 \\ D=q^2-4pr=10^2-4\cdot 1\cdot 24=4 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{10\pm \sqrt{4}}{2} \\ {a}_{1,2}=\frac{10\pm 2}{2} \\ {a}_{1,2}=5\pm 1 \\ {a}_1=6 \\ {a}_2=4 \\ a=a_1=6\text{cm} \\ b=10-a=10-6=4\text{cm} \\ u=\sqrt{a^2+b^2}=\sqrt{6^2+4^2}=2\sqrt{13}=7.2111\text{cm} \end{gathered}$$

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