Question

The diagonal of a rectangular field is 10 metres more than the shorter side. If the longer side is 5 metres more than the shorter side, find the length of the diagonal .

Answer 1

Answer:

25 m

Step-by-step explanation:

Let the length of the diagonal be x metre. According to the question, the breadth (shorter side) of the field is x-10 and the length (longer side) of the field is x-5. Since, length, breadth and diagonal of a rectangle form a right angle triangle, applying Pythagoras theorem we have

${(x - 5)}^{2} + {(x - 10)}^{2} = {x}^{2}$

$( {x}^{2} - 10x + 25) + ( {x}^{2} - 20x + 125) = {x}^{2}$

Simplifying we get a quadratic equation

${x}^{2} - 30x - 125 = 0$

Solving by factorisation method

${x}^{2} - 5x - 25x + 125 = 0$

$x(x - 5) - 25(x - 5) = 0$

$(x - 5)(x - 25) = 0$

$x = 25$

Note that x=5 is rejected as the length will become 0 and breadth will be -5 which is not possible.