Question
15 The rectangular frame for a wall of a new building is 7.5 m high and 18 m long. It has one
diagonal support. If the frame, including the diagonal support, is constructed from steel
girders that come in 10 m lengths, find the cost of the frame if the girders cost
diagonal support. If the frame, including the diagonal support, is constructed from steel
girders that come in 10 m lengths, find the cost of the frame if the girders cost
Ask by Nunez Boyd. in Australia
Feb 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
整个框架需要70.5米的钢梁，购买8节10米的钢梁，每节230美元，总成本是1840美元。
Solution
计算矩形框的总长度时，应包括四边和一个对角线支撑。
-
长方形的两边长分别为 18 m 和 7.5 m，故四边的总长度为
2 × (18 m + 7.5 m) = 2 × 25.5 m = 51 m。 -
对角线的长度为
√(18² + 7.5²) = √(324 + 56.25) = √380.25 = 19.5 m。 -
因此整个结构所需的钢梁总长为
51 m + 19.5 m = 70.5 m。
因为钢梁以 10 m 为一节出售，需要购买完整的 10 m 长度。计算需要的钢梁数量时，应向上取整：
70.5 m / 10 m = 7.05 节，因此实际应购买 8 节。
70.5 m / 10 m = 7.05 节，因此实际应购买 8 节。
每节钢梁的价格为 $230，所以总成本为
8 × $230 = $1840。
8 × $230 = $1840。
答：构造该框架的费用为 $1840。
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
To find the cost of the frame, we first need to calculate the total length of girders required for the rectangular frame and the diagonal support.
The perimeter of the rectangular frame is given by:
Next, we need to find the length of the diagonal support using the Pythagorean theorem:
Now, the total length of steel girders required is:
Since each girder is 10 m, the number of girders needed is:
Now, we can find the total cost:
So, the cost of the frame is
