Question

the perimeter of a rectangle is 12cm. The area 5cm². What is the length of the side​

Answer 1

Answer:

${ \underline{ \bold{ \green{Given:-}}}}$

• Perimeter of rectangle = 12cm
• Area of rectangle = 5cm²

${ \underline{ \bold{ \orange{Find:-}}}}$

• Length of side

${ \underline{ \bold{ \blue{Solution:-}}}}$

${ \boxed{ \bold{perimeter \: = 2(l + b)}}}$

${ \to{ \sf{2(l + b) = 12}}}$

${ \to{ \sf{l + b = \frac{12}{2} }}}$

${ \to{ \sf{l + b = 6}}}$

${ \to{ \sf{b = 6 - l.......(1)}}}$

${ \boxed{ \bold{area = l \times b}}}$

${ \to{ \sf{l \times b = 5}}}$

${ \to{ \sf{b = \frac{5}{L}.......(2)}}}$

From equation (1) and (2)

${ \to{ \sf{6 - L= \frac{5}{L} }}}$

${ \to{ \sf{L(6 - L) = 5}}}$

${ \to{ \sf{6L - {L}^{2} = 5 }}}$

${ \to{ \sf{ {L}^{2} - 6L + 5 = 0}}}$

${ \to{ \sf{ {L}^{2} - 5L + 1L + 5 = 0 }}}$

${ \to{ \sf{L(L - 5) - 1(L - 5)}}}$

${ \to{ \sf{(L- 5)(L- 1)}}}$

${ \sf{L - 1 = 0 \: { \to{L= 1}}}}$

Now substitute L value in equation (2)

${ \to { \sf{b = \frac{5}{L} }}}$

${ \to{ \sf{b = \frac{5}{1} = 5}}}$

So the length of side of rectangle is 5cm×1cm