A rectangular piece of land has a length of \((x+5)\) m and a width of \((2x-3)\) m.
A straight concrete path runs diagonally across the land from one corner to the opposite corner.
The length of this diagonal path is exactly \(20\) m.
Show that \(5x^2-2x-366=0\).[3]
Solve the equation \(5x^2-2x-366=0\).[3]
Hence find the perimeter of the rectangular piece of land, giving your answer correct to 1 decimal place.[3]
A contractor claims that if the diagonal path is increased to \(40\) m while keeping the exact same algebraic expressions for the length and width, the new value of \(x\) will be exactly double the positive value found in part (b).
Without solving the new equation, explain mathematically why the contractor’s claim is incorrect.[1]