Question

60. The length of a hall is 3 metres more than its breadth .If the area of the
hall is 238 sq metres, calculate its length and breadth.​

Answer 1

Answer:

Let breadth of hall be a m

Then length of hall = a + 3 m

Given :

Area of hall = 238 m²

i.e. Length × Breadth = 238 m²

( a + 3 ) ( a ) = 238

a² + 3 a = 238

a² + 3 a - 238 = 0

a² + 17 a - 14 a - 238 = 0

( a + 17 ) ( a - 14 ) = 0

a = - 17 or a = 14 .

Since side can't be negative .

Therefore , Length of hall is 17 m and breadth of hall is 14 cm .

Answer 2

$\huge\mathbb{\underline{\red{SOLUTION:-}}}$

Given the area of hall is 238 sq.m

and the length is x+3

and the breadth is x

$\sf\underline{\underline{\red{According \:to \: question}}}$

we know that the area of rectangle =Length ×breadth

Now the length is x+3 and breadth=x

Then :-

$\sf x(x+3)=238\\ \sf\implies x{}^{2}+3x=238\\ \sf\implies x{}^{2}+3x-238=0\\ \sf its \: become\: quadratic\: equation\\ \sf\implies By\: middle\:split\:term\\ \sf\implies x{}^{2}+3x-238=0\\ \sf\implies x{}^{2}+(17-14)x-238=0\\ \sf\implies x{}^{2}+17x-14x-238=0\\ \sf\implies x(x+17)-14(x+17)=0\\ \sf\implies (x+17)(x-14)=0$

$\sf\underline{\underline{\red{ZERO'S:-}}}$

$\sf i) x+17=0\\ \sf x=(-17)\\ \sf ii) x-14=0\\ \sf x=14$

x=(-17) or x=14

but the side can't be negative

so x=14

The length of hall =14+3=17 m

and the breadth =14 m

$\boxed{\underline{\red{\sf{Verification:-}}}}$

Area of rectangle= L×B

238=17×14

230 =238

$\underline{\red{\sf{Length=17m\: Breadth=14m}}}$