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Answer 1 · 2018-01-03T06:17:18

length = $10 c m$ $10 cm$ and width = $6 c m$ $6cm$

Suppose the width of the rectangle = $x c m$ $x cm$
Then, the length of the rectangle = $x + 4 c m$ $x+4 cm$

Now, the changes to the length and width of the rectangle are as below:

Length is decreased by $5 c m$ $5cm$ , then the new length will be:
$x + 4 - 5 c m$ $x+4 -5cm$ = $x - 1 c m$ $x-1 cm$

The width is decreased by $2 c m$ $2 cm$ , then the new width will be:
$x - 2 c m$ $x-2 cm$

The perimeter of this new rectangle = $18 c m$ $18 cm$

Perimeter of rectangle = $2 (l + w)$ $2(l+w)$
where, $l$ $l$ = length, and $w$ $w$ = width

So, $18$ $18$ = $2 \times [(x - 1) + (x - 2)]$ $2 xx[(x-1)+(x-2)]$
or, $18$ $18$ = $2 \times (2 x - 3)$ $2xx(2x-3)$ = $4 x - 6$ $4x-6$

or, $18$ $18$ = $4 x - 6$ $4x-6$

or, $18 + 6$ $18+6$ = $4 x$ $4x$

or, $x$ $x$ = $\frac{24}{4}$ $24/4$ = $6 c m$ $6 cm$ (width)

and length = $x + 4 c m$ $x+4 cm$ = $6 + 4 c m$ $6+4 cm$ = $10 c m$ $10 cm$