Question

There are two squares with integer side lengths a and b. 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?

Answer 1

24

Explanation:

4a+2b= 86 cm

a²+b²= 386 cm²

a+b=?

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• 4a+2b= 86
• 2a+b= 43
• (2a+b)²=43²
• 4a²+4ab+b²=1849

b²= 386- a², b= 43- 2a

• 4a²+4a(43-2a)+386-a²-1849=0
• 4a²+172a-8a²-a²-1463=0
• -5a²+172a-1463=0
• 5a²-172a+1463=0

solving quadratic equation we get

a=19 - integer solution

b= 43-2*19= 5

a+b=19+5=24