Question

The diagonal of a rectangular field is 60 metres more than the shorter side. If the larger side is 30 metres the shorter side, find the. dides of the field. ​

Answer 1

Answer:

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 fiel

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

Step-by-step explanation:

Answer 2

Solution :

$\bf{\orange{\underline{\bf{Given\::}}}}$

The diagonal of a rectangular field is 60 m more than the shorter side. If the larger side is 30 m the shorter side.

$\bf{\orange{\underline{\bf{To\:find\::}}}}$

The sides of the field.

$\bf{\orange{\underline{\bf{Explanation\::}}}}$

Let the shorter side be r m

Let the larger side be (r+30) m

We know that formula of the diagonal of rectangle :

$\boxed{\sf{Diagonal\:(d)=\sqrt{l^{2} +b^{2} } }}}$

A/q

$\longrightarrow\sf{\sqrt{l^{2} +b^{2} } =(r+60)m}\\\\\longrightarrow\sf{l^{2}+r^{2} =(r+60)^{2} }\\\\\longrightarrow\sf{l^{2} +r^{2} =r^{2} +60^{2} +2\times r\times 60}\\\\\longrightarrow\sf{l^{2} +\cancel{r^{2}} =\cancel{r^{2}} +3600+120r}\\\\\longrightarrow\sf{l^{2} =3600+120r}\\\\\longrightarrow\sf{(r+30)^{2} =3600+120r\:\:\:\:[given]}\\\\\longrightarrow\sf{r^{2} +30^{2} +2\times r\times 30=3600+120r}\\\\\longrightarrow\sf{r^{2} +900+60r=3600+120r}$

$\longrightarrow\sf{r^{2} +60r-120r+900-3600=0}\\\\\longrightarrow\sf{r^{2} -60r-2700=0}\\\\\longrightarrow\sf{r^{2} -90r+30r-2700=0}\\\\\longrightarrow\sf{r(r-90)+30(r-90)=0}\\\\\longrightarrow\sf{(r-90)(r+30)=0}\\\\\longrightarrow\sf{r-90=0\:\:Or\:\:r+30=0}\\\\\longrightarrow\sf{\red{r=90\:\:Or\:\:r=-30}}$

We know that negative value isn't acceptable .

Thus;

r = 90 m

$\underline{\sf{The\:Shorter\:side\:of\:field=r=90\:m}}}}}\\\underline{\sf{The\:Larger\:side\:of\:field=(r+30)=90+30=120\:m}}}}}$