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If AB=30, AC=40, and DE=24, what is the length of DF?

Please answer ASAP, I’m very behind in math.

If AB=30, AC=40, and DE=24, what is the length of DF? Please answer ASAP, I’m very-example-1
User Fmgp
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1 Answer

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Triangles ABC and DEF are similar with corresponding sides in proportion. Solving the ratio (30/24) = (40/x) yields x = 32. Thus, the length of DF is 32 units.

To solve this problem, we can use the properties of similar triangles. Triangles ABC and DEF are similar since they both have a 90-degree angle and an angle of 35 degrees.

The corresponding sides of similar triangles are proportional. Let's denote the length of DF as x. Then, we can set up a proportion using the corresponding sides:

(AB / DE) = (AC / DF)

Substitute the given values:

(30 / 24) = (40 / x)

Now, cross-multiply to solve for x:

30 * x = 24 * 40

30x = 960

x = 960 / 30

x = 32

Therefore, the length of DF is 32 units.

Complete question:

In ΔABC, m∠A = 90º and m∠B = 35º. In ΔDEF, m∠E = 35º and m∠F = 55º. If AB=30, AC=40, and DE=24, what is the length of DF?

User Pramod Kharade
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8.1k points

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