Question

The diagonal 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

Step-by-step explanation:

Let the length of the shorter side be x metres.

The length of the diagonal= 60+x metres

The length of the longer side =30+x metres

Applying Pythagoras theorem,

Diagonal²=longer side²+shorter side²

(60+x) ²= (30+x) ² + x²

3600+120x+x²=900+60x+x²+x²

2700+60x-x²=0

2700+90x-30x-x²=0

90(30+x)-x(30+x) =0

X=90,

Shorter side is 90m, longer side is 90+30=120m

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Answer 2

★$\huge\tt{Answer}$★

$\sf\color{red}$Let the shorter side of the rectangle be x m.

$\sf\color{red}$Then, larger side of the rectangle = (x + 30) m

➦$\sf\color{red}$ x2 + (x + 30)2 = (x + 60)2

➦ $\sf\color{red}$x2 + x2 + 900 + 60x = x2 + 3600 + 120x

➦$\sf\color{red} x2 -\: 60x - \:2700\: = 0</p><p>$

➦$\sf\color{red}x2 - \:90x +\: 30x - \:2700 \:= 0$

➦$\sf\color{red} x\:(x - 90) + \:30(x -90)$

➦$\sf\color{red}(x - 90)\:(x + 30)\: = 0$

➦$\sf\color{red}x = 90,\: -30$

$\sf\color{red}However, \:side\: cannot\: be \:negative.\: Therefore\:, the\: length \:of \:the \:shorter\: side\: will\: be\: 90 m.$

$\sf\color{red}Hence,\: length\: of\: the \:larger \:side \:will \:be\: (90 + 30)$

$\bold\pink{\fbox{\sf{m = 120 m.}}}$

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All done :)

Thankyou :)