Question

The diagonals of a rectangular field is 60 metres more than the shorter side.
If the longer side is 30 metres more than the shorter side, find the sides
of the field.​

Answer 1

Answer:

the sides are 270 and 90

Step-by-step explanation:

using Pythagoras theorem

${(60 + x)}^{2} = {(30 + x)}^{2} + {x}^{2}$

$3600 + {x}^{2} + 120x = 900 + {x}^{2} + 60x + {x}^{2}$

$3600 - 900 + 120x - 60x = 2 {x}^{2} - {x}^{2}$

${x}^{2} - 60x - 2700 = 0$

${x}^{2} - 90x + 30x - 2700$

$x(x - 90) + 30(x - 90)$

$(x + 30)(x - 90)$

$x = 90$

$30 + x = 270$

Answer 2

$\bf{\underline{\underline{Question}}}$

$\:$

The diagonals of a rectangular field is 60 metres more than the shorter side.

If the longer side is 30 metres more than the shorter side, find the sides

of the field.

$\:$

$\bf{\underline{\underline{Solution}}}$

$\:$

$\small\tt{Shorter\:side \:of \:field\:=\:x\:=\:90\:m}$

$\:$

$\small\tt{Longer\:side \:of \:field\:=\:x\:+\:30}\\{\small\tt{\:=\:90\:+\:30\:=\:120\:m}}$

$\:$

$\bf{\underline{\underline{Thanks}}}$

$\:$