Question

the perimeter of a pentagon is 30 cm. If four of its sides measure 55 mm, 11 cm 4 mm, 4 cm 6 mm and 45 mm find the length of fifth side.​

Answer 1

Given,

Perimeter of a pentagon is $30cm$

Four sides of a pentagon $a,b,c,d,e$

$a=55mm=5.5cm$

$b=11cm4mm=11+0.4=11.4cm$

$c=4cm6mm=4+0.6=4.6cm$

$d=45mm=4.5cm$

We have to find $e$

The perimeter of pentagon is $a+b+c+d+e=30cm$

$5.5+11.4+4.6+4.5+c=30$

$26+c=30$

$c=30-26$

$c=4$

Therefore, the fifth side of a pentagon is $4cm$

Answer 2

Given,

The perimeter of a pentagon is $30cm$. If four of its sides measure $55mm$, $11cm4mm$, $4cm6mm$ and $45mm$.

Formula,

Perimeter of a pentagon $=a+b+c+d+e$

To convert millimeters into centimeters

$55mm=5.5cm$

$11cm4mm=11.4cm$

$4cm6mm=4.6cm$

$45mm=4.5cm$

Substitute above values in formula,

$P=5.5+11.4+4.6+4.5+e$

$30=26+e$

$e=4cm$

Therefore, the length of fifth side is $4cm$.