Question

A rectangle with perimeter 44 cm is partioned into5 congruent rectangles as indicated in the diagram The perimeter of each of the congruent rectangle ?

Answer 1

Given: Perimeter $=44$cm

Let the length of each small rectangle be l and breadth be b,

Perimeter of rectangle $2(l+b)=44$

Now, according to figure,

Perimeter is,

$=b+b+b+l+b+l+l+b+l=44$

$=5b+4l=44$ $......\left(1\right)$

Also, from figure it is clear that 3 breadth of top vertical rectangles is equal to 2 lengths of bottom horizontal rectangle

$\Rightarrow 3b=2l$ $.......\left(2\right)$

Now put $3b=2l$ in equation (1),

$\therefore$ $5b+4l=44$

$\Rightarrow 5b+2\ast 2l=44$

$\Rightarrow 5b+2\ast 3b=44$

$\Rightarrow 5b+6b=44$

$\Rightarrow 11b=44$

$\Rightarrow b=4$

Therefore, from equ..(2), we get

$3\ast 4=2l\Rightarrow 12=2l\Rightarrow l=6$

$\Rightarrow l=6$ and $b=4$

The perimeter of each of the congruent rectangle $=2(l+b)$

$=2(6+4)=12+8=20$

Hence perimeter of each small rectangle will be 20.