The area of a rectangle fountain is (x^2 + 12x + 20) square feet. a 2-foot walkway is built around the fountain. find the dimensions of the outside border of the walkway.

Length=x+14 ft

Width=x+6 ft

Step-by-step explanation:

Step 1

Information provided

Step 2

By factorization

Area=x(x+2)+10(x+2)

Notice that x+2 are common on RHS therefore,

Area=(x+2)(x+10)

Since the length is usually longer than width, then x+10 is taken as original length, x+2 is the original width.

Step 3

When a 2-ft walkway is built, dimensions of outside border increase by 2ft+2ft=4ft

Therefore, length=x+10+4=x+14 ft

Width=x+2+4=x+6 ft

Ans

Length=x+14 ft

Width=x+6 ft

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm