To Calculate:
The width x of a strip around the rectangular patio.
x=3.5 ft
Given:
The dimensions of rectangular patio are 25 ft by 40 ft .
This patio is surrounded by a terraced strip of uniform width x and area 504 ft2 .
Concepts Used:
The area of a rectangle is the product of its length and width.
Calculations:
Draw a figure representing the given situation. Shade the area representing the terraced strip.
The outer rectangle has a width 40+2x and length 25+2x . The area of the outer rectangle is given to be 504 ft2 . Substitute this information in the formula for area of shaded region, namely the outer rectangle less the inner rectangle, and solve the resulting equation for x .
Shaded area=504Area of outer rectangle − Area of inner rectangle=504(40+2x)(25+2x)−25×40=5041000+80x+50x+4x2−1000=5044x2+130x−504=02x2+65x−252=02x2−7x+72x−252=0x(2x−7)+36(2x−7)=0(2x−7)(x+36)=0x=3.5,−36
Only positive value of width makes sense so x=3.5 .
Conclusion:
The width of a strip around the rectangular patio is x=3.5 ft .
Chapter 2 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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