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Joe_1234
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A trapezoid with a base of 100m and 160m is divided into 2 equal parts by a line parallel to the base. Find the length of dividing line.
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Yes. TnxMarkFL said:Let's let the larger base be \(B\), the smaller base be \(b\) and the height be \(h\).
I would consider how long a line will be that cuts the trapezoid parallel to the bases. We know this length \(L\) will decrease linearly as we move from \(0\) to \(h\), and in fact, the line will contain the points:
\(\displaystyle L(0)=B\)
\(\displaystyle L(h)=b\)
And so:
\(\displaystyle L(y)=\frac{b-B}{h}y+B\)
Now, we require:
\(\displaystyle \frac{y}{2}(B+L(y))=\frac{h}{4}(B+b)\)
\(\displaystyle \frac{y}{2}\left(B+\frac{b-B}{h}y+B\right)=\frac{h}{4}(B+b)\)
\(\displaystyle 2y\left(B+\frac{b-B}{h}y+B\right)=h(B+b)\)
\(\displaystyle 2y(2Bh+(b-B)y)=h^2(B+b)\)
Arrange as quadratic in \(y\) in standard form:
\(\displaystyle 2(B-b)y^2-4Bhy+h^2(B+b)=0\)
Can you proceed?
To find the length of a dividing line in a trapezoid, you can use the formula: (a + b) / 2, where a and b are the lengths of the parallel sides of the trapezoid. This formula works for both right and non-right trapezoids.
No, the Pythagorean theorem only applies to right triangles. It cannot be used to find the length of a dividing line in a trapezoid.
If the trapezoid has unequal parallel sides, you can still use the formula (a + b) / 2 to find the length of the dividing line. However, a and b will represent the lengths of the two unequal parallel sides.
Yes, you can use the area of a trapezoid to find the length of a dividing line. The formula for the area of a trapezoid is (a + b) * h / 2, where a and b are the lengths of the parallel sides and h is the height of the trapezoid. You can rearrange this formula to solve for the length of the dividing line by substituting the known values for the area, parallel sides, and height.
No, the length of the dividing line can be measured in any unit of length, such as inches, centimeters, or feet. It is important to use the same unit of measurement for all the lengths involved in the calculation to ensure accuracy.