Question

100 points!!!!!

If the area of C is
400 ft2 and the
perimeter of B is 64 ft,
what is the side length
of square A?

Answer 1

`\\\text{Side length of square A = a \text{ft}}\\\\\text{Side length of square B = b \text{ft}}\\\\ \text{Side length of square C = c \text{ft}}\\\\ \text{Given that,}\\\\\text{Area of square C} = 400 ~ \text{ft}^2\\\\\implies c^2=400~~~~~~......(i)\\\\\\\text{Perimeter of square B } = 64~ \text{ft}\\\\\implies 4b = 64\\\\\implies b = \frac{64}4\\\\\implies b = 16\\\\\implies b^2 = 256~~~~~~~.....(ii)\\\\\\`

`\text{Applying Pythagorean theorem,}\\ \\~~~~~c^2 =a^2 +b^2\\\\\implies a = √(c^2 - b^2)\\ \\\implies a = √(400-256)\\\\\implies a = √(144)\\\\\implies a = 12`

`\text{Hence, the side length of square A is 12 ft.}`