Question

The length of a rectangle is 5 cm longer than its width and its area is 66 cm². Find the perimeter of the
rectangle.​

Answer 1

Width =X

Length=5+X

Area= length ×width

66=X×(5+X)

66=5X+X^2

X^2+5X-66=0

By solving this quadratic expression you will get X =6

Width=6cm

Length=6+5=11cm

Please mark me Priya list and thank my 4 answers because I am giving my precious time for helping you

Answer 2

Step-by-step explanation:

Let width is x cm

then length = x+5 cm

Area of rectangle = Length × width

$area \: \: = 66 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x(x + 5) = 66 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ {x}^{2} + 5x = 66 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ {x}^{2} + 5x - 66 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ {x}^{2} + 11x - 6x - 66 = 0 \\ \\ x(x + 11) - 6(x + 11) = 0 \\ \\ (x - 6)(x + 11) = 0 \: \: \: \: \: \: \: \: \: \: \: \ \\ then \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x = 6 \: \: or \: \: - 11$

Since length can't be negative then

x= 6 cm

length = 6+5 = 11 cm

width = 5 cm

perimeter = 2( length + width)

= 2(11+5)

= 32 cm