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:

Answer Expert Verified

And the length of the diagonal will be (x + 60) meters. ... x = 90 because x = - 30 as length cannot be possible. So the length of the shorter side is 90 meters and the length of the longer side is 90 + 30 = 120 meters. Answer.

Answer 2

Given : The diagonal of a rectangular field is 60 metres more than the shorter side & The longer side is 30 metres more than the shorter side.

To Find : Find the sides of the field ?

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Solution : Let shorter side be x m

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• $\leadsto$diagonal = ( x + 60) m
• $\leadsto$longer side = (x + 30) m

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$\underline{\frak{As ~we ~know~ that~:}}$

◗${\sf{In ~right~triangle~ ABC}}$

• $\boxed{\sf\pink{(AC)^2~=~ (AB^2~+ ~(BC)^2}}$★

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${\sf:\implies{(x + 60)^2~= ~(x)^2~ +~ (x ~+ ~30)^2}}$

${\sf:\implies{(x)^2~ + ~2 ~×~ x~ × ~60~ + ~(60)^2~ = ~x^2~+ ~(x)^2~ + ~2~ ×~ x~ × ~30 ~+ ~(30)^2}}$

${\sf:\implies{x^2~ + ~120x ~+ ~3600 ~= ~x^2~ + ~x^2~ + ~60x ~+ ~900}}$

${\sf:\implies{x^2~+~ 60x~ + ~900~ - ~120x ~- ~3600~ = ~0}}$

${\sf:\implies{x^2~ - ~60x~ -~ 2700~ =~ 0}}$

${\sf:\implies{x^2~ - ~90x ~- ~30x~ -~ 2700 ~= ~0}}$

${\sf:\implies{x(x~ - ~9) ~+ ~30(x~ - ~90) ~= ~0}}$

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

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Now,

• ${\sf\dashrightarrow{(x ~-~ 90) ~=~ 0}}$
• ${\sf\dashrightarrow{x ~= ~0 +~ 90}}$
• ${\sf\dashrightarrow{x ~= ~90}}$

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Then,

• ${\sf\dashrightarrow{(x ~+ ~30) ~= ~0}}$
• ${\sf\dashrightarrow{x ~= ~0 - ~30}}$
• ${\sf\dashrightarrow{x~ = ~- 30}}$

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Therefore,

• The side of the field cannot be negative so, the length of the shorter side will be 90 m and length of longer side will be (x + 30) = (90 + 30) = 120 m.

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Hence,

$\therefore\underline{\sf{The~length~of~longer~side~will~be~\bf{\underline{120~m}}}}$