+114 The perimeter of the entire figure is 86 cm, and the sum of the areas of the two squares is 386 cm^2. In centimeters, what is the value of a + b ?
+129849 We have that
3a + (a - b) + 3b = 86
4a + 2b = 86 divide through by 2
2a + b = 43
b = 43 - 2a (1)
and
a^2 + b^2 = 386 (2) sub (1) into (2) for b
a^2 + (43 - 2a)^2 = 386 simplify
a^2 + 4a^2 - 172a + 1849 = 386 subtract 386 from both sides
5a^2 - 172a + 1463 = 0 this will factor as
(5a - 77) (a - 19) = 0
The second factor set to 0 and solved for "a" gives us an integer solution....
a =19
And b = 43 - 2(19) = 5
So.....a + b = 24
