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This is Pythagorean theorem P is 105ft Q is 208 what is the length of PQ
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Answered by
GPT 3.5
To find the length of PQ using the Pythagorean theorem, we need to label the sides of a right triangle.
According to the Pythagorean theorem, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's assume that the length of PQ is 'c' (the hypotenuse), and the lengths of the other two sides are 'a' and 'b'.
According to the given information, P = 105 ft, and Q = 208 ft.
Applying the Pythagorean theorem:
a^2 + b^2 = c^2
(105 ft)^2 + (208 ft)^2 = c^2
11025 ft^2 + 43264 ft^2 = c^2
54289 ft^2 = c^2
Taking the square root on both sides to solve for c:
c = √54289
c ≈ 232.91 ft
Therefore, the length of PQ (c) is approximately 232.91 ft.
According to the Pythagorean theorem, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's assume that the length of PQ is 'c' (the hypotenuse), and the lengths of the other two sides are 'a' and 'b'.
According to the given information, P = 105 ft, and Q = 208 ft.
Applying the Pythagorean theorem:
a^2 + b^2 = c^2
(105 ft)^2 + (208 ft)^2 = c^2
11025 ft^2 + 43264 ft^2 = c^2
54289 ft^2 = c^2
Taking the square root on both sides to solve for c:
c = √54289
c ≈ 232.91 ft
Therefore, the length of PQ (c) is approximately 232.91 ft.
Answered by
GPT 3.5
Yes, if you round to the nearest whole number, the length of PQ would be 233 ft.
Answered by
GPT 3.5
To find the area of the triangle, we can use the formula:
Area = (1/2) * base * height
In the given information, we have the lengths of two sides of the triangle (105 ft and 208 ft), but we need to find the length of the third side (PQ) to calculate the area accurately.
From the previous calculation, we found that the length of PQ is approximately 232.91 ft (or rounded to 233 ft).
Now, we can choose any two sides of the triangle as the base and height. Let's choose PQ as the base (with length 233 ft) and P as the height (with length 105 ft).
Plugging these values into the formula:
Area = (1/2) * base * height
= (1/2) * 233 ft * 105 ft
= 12232.5 ft^2
Therefore, the area of the triangle is approximately 12232.5 square feet.
Area = (1/2) * base * height
In the given information, we have the lengths of two sides of the triangle (105 ft and 208 ft), but we need to find the length of the third side (PQ) to calculate the area accurately.
From the previous calculation, we found that the length of PQ is approximately 232.91 ft (or rounded to 233 ft).
Now, we can choose any two sides of the triangle as the base and height. Let's choose PQ as the base (with length 233 ft) and P as the height (with length 105 ft).
Plugging these values into the formula:
Area = (1/2) * base * height
= (1/2) * 233 ft * 105 ft
= 12232.5 ft^2
Therefore, the area of the triangle is approximately 12232.5 square feet.
Answered by
GPT 3.5
If it was a rectangle, we would need the lengths of both the width and height to calculate the area. However, the given information only provides the lengths of two sides (105 ft and 208 ft) but not their orientations.
Without knowing the orientation of the sides, we cannot determine which one is the width and which one is the height. Therefore, we cannot calculate the area of the rectangle with the given information.
Without knowing the orientation of the sides, we cannot determine which one is the width and which one is the height. Therefore, we cannot calculate the area of the rectangle with the given information.
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