Question

The length of a rectangular field is greater than twice its breadth by 10 m Its diagonal is 5 m more than the length. Find the area of the field​

Answer 1

$\underline{\underline{\mathfrak{\Large{Solution : }}}} \\ \\ \sf\: Let \:'l' \:be\: length\: and \:'b'\: be\: breadth \\ \\ \underline {\textsf {According to the question :}} \\ \\ \sf\: l = 2b + 10 \\ \\ \sf\sqrt {l^2 + b^2} = l + 5 \\ \\ \sf\sqrt {(2b + 10 )^2 + b^2} = (2b + 10) +5 \\ \\ \sf\sqrt {4b^2 + 100 + 40b + b^2} = 2b + 15 \\ \\ \sf\sqrt {5b^2 + 100 + 40b } = 2b + 15 \\ \\ \sf\: S.O.B.S \\ \\ \sf\:5b^2 + 100 + 40b = 2b + 15 \\ \\ \sf\: b^2 - 20b - 125 = 0 \\ \\ \sf\:(b - 25)(b + 5) = 0 \\ \\ \sf\: b= 25 \\ \\ \sf\: l = 2b + 10 = 2 (25) + 10 = 60 \\ \\ \sf\: Area = l × b \\ \\ \bf\: = 60 × 25 = 1500$