Question

If the length of a certain rectangle is decreased by 4 cm and width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.​

Answer 1

QUESTION

If the length of a certain rectangle is decreased by 4 cm and width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.

FIND

The perimeter of original rectangle =?

Answer

50 cm^2

Explanation

• let the length be X cm.
• and breadth be Y cm

★According to Question★

$\bf x \: - 4 = y + 3 \ \\ \: \bf \ x - y = 7........(1)eq$

And

$\bf x.y + 3x - 4y - 12 = x .y \\ \: \: \: \: \bf or \\ \: \bf 3x - 4y = 12......(2)eq$

From equation (i) and (ii)

$\large \bf \frac{x}{ - 12 + 28} = \frac{y}{21 - 12} = \frac{ - 1}{ - 4 + 3}$

oR

$\large \bf \frac{x}{16} = \frac{y}{9} = 1$

● so x=16cm

●and y= 9 cm

★Therefore the perimeter of original rectangle

= 2.(16+9)= 50cm

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Perimeter\:of\:original\:triangle=50\:cm}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline{\bold{Given :}}} \\ \tt: \implies Length \: of \: rectangle \: decreased \: by \: 4 \: cm \\ \\ \tt: \implies Width\: of \: rectangle \: increased \: by \: 3\: cm \\ \\ \red{\underline{\bold{To \: Find :}}} \\ \tt: \implies Perimeter \: of \:original \:rectangle =M$

• According to given question :

$\green{\star } \tt \: Let \: length \: be \: 'l' \\ \\\green{\star } \tt \: \: Breadth \: be \: 'b' \\ \\\green{\star } \tt \: New \: length = l - 4\\ \\ \green{\star } \tt \: New \: breadth = b +3\\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies New \: length \: = New \: breadth \: \: \: \: \\ \\ \tt: \implies l - 4 = b +3 \\ \\ \tt: \implies l - b = 7 - - - - - (1) \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: new \: rectangle = Area \: of \: original\:rectangle \\ \\ \tt: \implies (l - 4)(b + 3) = l \times b \\ \\ \tt: \implies lb - 4b + 3l - 12 =lb \\ \\ \tt: \implies 3l - 4b = 12 - - - - - (2) \\ \\ \text{Solving \: (1) \: and \: (2)}$

$\tt: \implies b = 9 \: \: \: and \: \: \:l = 16 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Perimeter \: of \: original \: rectangle =2(l + b) \\ \\ \tt: \implies Perimeter \: of \: original \: rectangle =2(16 + 9) \\ \\ \tt: \implies Perimeter \: of \: orginal \: rectangle =2 \times 25 \\ \\ \green{\tt: \implies Perimeter \: of \: original\: rectangle =50 \: cm}$