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natali 33 [55]
2 years ago
9

100 points!!!!!

Mathematics
1 answer:
Zina [86]2 years ago
6 0

\\\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 = \dfrac{64}4\\\\\implies b = 16\\\\\implies b^2 = 256~~~~~~~.....(ii)\\\\\\

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

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

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Next, let's find the y coordinate distance change. We move from the y coordinate 0, to the y coordinate 4, <u>so we move 4 y units.</u>

Now that we have these two leg lengths, let's imagine this as a right triangle. Moving from the origin, we draw a line from (0,0), to (-8,0). Then, we draw a line from (-8,0) to (-8,4). Now, draw a direct line from (0,0), to (-8,4). We have the length of the first(8) and second(4) lines, and we need to find the third line length to find our answer. To do this, we use the Pythagorean Theorem, which states that a²+b²=c². This says that, in a right triangle, the square of the two shorter lengths equals the square of the longest length. The longest length is what we are solving for.

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