Rectangle Garden Area Diagonals

The length of the sides of the rectangular garden is 4:3. The line segment connecting the midpoints of adjacent sides is 20 m long. Calculate the area of the garden.

Final Answer:

S =  768 m²

Step-by-step explanation:

$$\begin{gathered} a:b=4:3 \\ 3a/4=b \\ (a/2{)}^2+(b/2{)}^2=20^2 \\ (a/2{)}^2+(3a/8{)}^2=20^2 \\ 0.390625a^2-400=0 \\ {a}_{1,2}=\pm \sqrt{400/0.390625}=\pm 32 \\ {a}_1=32 \\ {a}_2=-32 \\ a>0 \\ a=a_1=32\text{m} \\ b=\frac{3}{4}\cdot a=\frac{3}{4}\cdot 32=\frac{3\cdot 32}{4}=\frac{96}{4}=24\text{m} \\ S=a\cdot b=32\cdot 24=768{\text{m}}^2 \end{gathered}$$

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