Question

The length of a rectangle flower bed is 5ft longer than its width. A sidewalk with a width of 3ft surrounds the bed. If the total area of the bed and sidewalk is 546ft^2, what are the dimensions of the flower bed ?

Answer 1

Answer:

$W=15ft$

$L=20ft$

Step-by-step explanation:

From the question we are told that:

Length of Bed $L=5+W$

Width of sidewalk $W_s=3ft$

Area of the bed and sidewalk $A_t= 546ft^2$

Generally the equation for Area of the bed and sidewalk$A_t$ is mathematically given by

 $Area=L*B$

 $A_t=((3+3)+L)*((3+3)+W)$

Therefore

 $546=((3+3)+(5+W))*((3+3)+W)$

 $0=((6+(5+W))*((6)+W)-546$

 $(11+W)*(6+W)-546=0$

 $W^2+17B-480=0$

Solving the Quadratic Equation

 $W=15ft$ (Using only positive root)

Generally the Length L is mathematically given by

 $L=5+15$

 $L=20ft$