The length of a rectangle is 5 meters more than twice the width. If the length of the diagonal is 5√97 m, what is the area?
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Sᴏʟᴜᴛɪᴏɴ :-
Let us Assume That , Breadth of Rectangle is x m.
Than,
→ Length = 2*x + 5 = (2x + 5)
So,
→ Diagonal of Rectangle = √[Length² + Breadth²]
A/q,
→ √[(2x + 5)² + x²] = 5√97
Squaring both sides,
→ 4x² + 25 + 20x + x² = 25 * 97
→ 5x² + 20x + 25 - 2425 = 0
→ 5x² + 20x - 2400 = 0
→ 5(x² + 4x - 480) = 0
→ x² + 4x - 480 = 0
→ x² + 24x - 20x - 480 = 0
→ x(x + 24) - 20(x + 24) = 0
→ (x + 24)(x - 20) = 0
→ x = (-24) or 20. { Negative value ≠ .}
Therefore,
→ Breadth of Rectangle = x = 20m.
→ Length of Rectangle = (2x + 5) = (2*20 + 5) = 40 + 5 = 45m.
Hence,
→ Area of Rectangle = Length * Breadth = 20 * 45 = 900m². (Ans.)
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