(a)
To find: The value of x.
The value of x is 9 cm.
Given:
The given figure is,
Figure (1)
The area of figure is 144 cm2 .
Calculation:
Tabulate the given information into the language of algebra.
Model the equation for the above information.
Area of part 1+Area of part 2=Total area10×x+6×x=144
Simplify the above equation for x,
10x+6x=14416x=144x=9
Thus, the value of x is 9 cm.
(b)
The value of x is 5 in.
Figure (2)
The area of figure is 160 in2 .
Area of part 1+Area of part 2=Total areax×(x+14)+13×x=160
x2+14x+13x=160x2+27x−160=0(x+32)(x−5)=0x=−32,x=5
The value of x cannot be negative.
Thus, the value of x is 5 in.
Precalculus: Mathematics for Calculus - 6th Edition