Question

8. A field is in the shape of a pentagon. The cost of fencing the field at the rate of 42 per metre is 6720. If the length of four sides are 28 m, 32 m, 40 m and 36 m, find the length of the fifth side.​

Answer 1

$\huge \purple{ \underline{ \boxed{ \red{ \mathbb{ANSWER : }}}}}$

$\red{ \textsf{Length of fifth side is \orange{24 m .}}}$

$\huge \purple{ \underline{ \boxed{ \red{ \mathbb{EXPLANATION : }}}}}$

$\large\green{ \underline{ \underline{ \mathbb{GIVEN : }}}}$

$\orange{ \textsf{Cost of fencing per metre = Rs.42}}$

$\orange{ \textsf{Total cost of fencing the field = Rs.6720 }}$

$\orange{ \textsf{Length of four sides = 28 m , 32 m , 36 m , 40 m}}$

$\large\green{ \underline{ \underline{ \mathbb{FORMULA \: USED : }}}}$

$\orange{ \textsf{Perimeter of pentagon = Sum of all sides}}$

$\orange{ \textsf{Total cost of fencing the field = Cost of fencing per metre x Perimeter of pentagon }}$

$\large\green{ \underline{ \underline{ \mathbb{SOLUTION : }}}}$

$\red{ \textsf{Let x be the fifth side . }}$

$\red{ \textsf{Therefore}}$

$\red{ \textsf{Total cost of fencing the field = Cost of fencing per metre x Perimeter of pentagon }}$

$\red{ \mathsf{ \implies 6720 = 42 \times (28 + 32 + 40 + 36 + x)}}$

$\red{ \mathsf{ \implies 6720 = 42 \times (136 + x)}}$

$\red{ \mathsf{ \implies \frac{6720}{42} = (136 + x)}}$

$\red{ \mathsf{ \implies 160 = (136 + x)}}$

$\red{ \mathsf{ \implies x = 160 - 136}}$

$\red{ \mathsf{ \implies x = \: 24 \: m}}$