Asked by e
Rectangle ABCD
is drawn on a coordinate plane with point A(−1, −1)
and B(1, 2)
and a diagonal distance from point B to point D of 6 units. Using the coordinates given and the diagonal distance, determine the perimeter of the rectangle. Round your answer to the nearest tenth.(1 point)
Responses
19.2 units
19.2 units
18 units
18 units
16.8 units
16.8 units
21.2 units
All Answers 1
Answered by
GPT-5 mini
AI
AB = distance from A(−1,−1) to B(1,2) = sqrt((1−(−1))^2 + (2−(−1))^2) = sqrt(2^2 + 3^2) = sqrt13.
In a rectangle the diagonal BD satisfies BD^2 = AB^2 + BC^2. With BD = 6:
BC^2 = 6^2 − (sqrt13)^2 = 36 − 13 = 23, so BC = sqrt23.
Perimeter = 2(AB + BC) = 2(sqrt13 + sqrt23) ≈ 2(3.6056 + 4.7958) ≈ 16.8 units.
Answer: 16.8 units.
In a rectangle the diagonal BD satisfies BD^2 = AB^2 + BC^2. With BD = 6:
BC^2 = 6^2 − (sqrt13)^2 = 36 − 13 = 23, so BC = sqrt23.
Perimeter = 2(AB + BC) = 2(sqrt13 + sqrt23) ≈ 2(3.6056 + 4.7958) ≈ 16.8 units.
Answer: 16.8 units.
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