Find the 4√2 side of the square.
| August 4, 2021 | education
The diagonal of the square splits it into 2 right-angled triangles, the legs of which are equal. Using the Pythagorean theorem, we find the leg:
a ^ 2 + b ^ 2 = c ^ 2.
Since a = b, then
a ^ 2 + a ^ 2 = c ^ 2;
2a ^ 2 = c ^ 2;
2a ^ 2 = (4√2) ^ 2;
2a ^ 2 = (√ (16 * 2) ^ 2;
2a ^ 2 = 16 * 2;
a ^ 2 = 16 * 2: 2;
a ^ 2 = 16;
a = √16;
a = 4.
Answer: The side of the square is 4.
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