Question

The length of a rectangle exceeds its breadth by 5 cm. If the length and breadth of the rectangle
are increased by 1 cm, the area increases by 34 cm?. Find the length and breadth of the rectangle.
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Answer 1

here is ur answer sweetie.please mark as brainliest.

let the breadth -(x)cm

then length - (x+5)cm

area- l multiplied by b.

so x(x+5)cm

x sq. +5x

then after changes,

breadth-(x+1) cm

then length - (x+5+1)cm

length- (x+6) cm

area - l*b

area-(x+1)(x+6)

area-x sq. +(1+6)x +1*6

area-x sq. +7x + 6

a.t.q.

the area increases by 34 cm

x sq. +5x+34=x sq. +7x+6

5x-7x = 6-34

-2x= -28/-2

x =14

breadth =14 cm

length=x+5 cm

14+5cm

19 cm

thank u

please humble request mark as brainliest.

Answer 2

$\huge{\boxed{\boxed{\red{\ulcorner{\mid{\overline{\underline{\bf{Answer:-}}}}}\mid}}}}$

$\large\red \rightarrow l = 19. \: \: and \: \: b \: = 14.$

°•° Let breadth be ( x cm )

$\star{Length = ( x + 5 ).}$

${Area = (l \times \: b) }$

${=(x+5)\:\times\: (x) }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 5.$

$\star{New Length = (x+5+1)}$

${=x+6}$

$\star{New Breadth = (x+1) cm}$

$\star{New Area = (l \: \times\: b)}$

${= (x+6)(x+1)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 7x + 6.$

Now,

$\star \: new \: area - original \: area \: = 34. \\ \\ {x}^{2} + 7x + 6 - ( {x}^{2} + 5x) = 34. \\ \\ \cancel{x}^{2} + 7x + 6 - \cancel {x}^{2} - 5x = 34. \\ \\ \rightarrow \: 2x = 28. \\ \\ \rightarrow \: x = \frac{ \cancel2 \cancel8}{ \cancel2} \\ \\ \rightarrow \: x = 14.$

So ,

$\star \: breath \: = 14 \: cm. \\ \\ \\ \\ \star \: length = 19 \: cm.$

$\huge \red \star \: \: \: thank \: \: \: you \: \: \: \red \star$

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