Question

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

Answer 1

Answer:-

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• Given:-

The diagonal of a rectangular field is $\bf{60 \: metres}$ more than the shorter side.

The longer side is $\bf{30 \: metres}$ more than the shorter side.

• To find :-

The sides of the field

• Solution :-

Let shorter side be $\bf{"x" \: m}$

Diagonal = $\bf{( x + 60) m}$

longer side = $\bf{(x + 30) m}$

In right $\triangle ABC$:-

By Pythagoras theorem:-

$(AC)^2 = (AB)^2 + (BC)^2$

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

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

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

$\longrightarrow{x^2 +120x +3600-2x^2 -60x-900=0}$

$\longrightarrow{-x^2+ 60x + 2700 = 0}$

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

$\longrightarrow{x^2 - 90x + 30x - 2700 = 0}$

$\longrightarrow{ x(x - 90) + 30(x - 90) = 0}$

$\implies{(x - 90) ( x + 30) = 0}$

Now,

$\longrightarrow{(x - 90) = 0}$

$\longrightarrow{x = 0 + 90}$

$\implies\bf{x = 90}$

Also,

$\longrightarrow{(x + 30) = 0}$

$\longrightarrow{ x = 0 - 30}$

$\implies{ x = -30}$

But length cannot be $\bf{negative}$

Hence, the length of the shorter side of the rectangular field will be $\bf{90 \: m}$.

and length of longer side will be (x + 30) = (90 + 30) = $\bf{120 \: m}$

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Answer 2

Answer:

GIVEN :-

• The diagonal of a rectangular field is 60m more than the shorter sides.
• the longer side is 30m more than the shorter side.

TO FIND :-

• find the sides if the field.

SOLUTION :-

• 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

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• 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 20 ➡️90+30=120m