Solve for the unknown length.
1 answer:
<h2>Similar Triangles</h2>
Similar triangles have the same proportions of sides, but they have different side lengths.
To solve for missing sides in similar triangles, we can set up a proportion.
For instance, let's say that side <em>a</em> in Triangle A corresponds with side <em>b</em> in Triangle B. Let's say that side <em>h</em> in Triangle A also corresponds with side <em>k</em> in Triangle B. Then, it would be true that:
We need to make sure of a couple things:
- The numerators and denominators of fractions are corresponding
- The numerators describe one triangle, and the denominators describe another (can't switch, otherwise the calculations will get messed up)
We're given two triangles (do you see it?).
- Triangle ABC
- Triangle ADE
These two triangles are similar.
We must solve for the length of side BC in Triangle ABC.
- We're given the length of DE, the corresponding side in Triangle ADE.
- We're also given the lengths of bottom sides, 20 units and 30 + 20 = 50 units.
Set up a proportion:
Therefore, the unknown length is 37.5 units.
<h2>Answer</h2>37.5 units
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Answer:
The length of side KM is units.
Step-by-step explanation:
Given information: KLMN is a trapezoid, ∠N= ∠KML, FD=8, LM:KN=3:5, F∈ KL, D∈ MN , ME ⊥ KN KF=FL, MD=DN, .
From the given information it is noticed that the point F and D are midpoints of KL and MN respectively. The height of the trapezoid is .
Midsegment is a line segment which connects the midpoints of not parallel sides. The length of midsegment of average of parallel lines.
Since LM:KN=3:5, therefore LM is 3x and KN is 5x.
Therefore the length of LM is 6 and length of KN is 10.
Draw perpendicular on KN form L and M.
(KA=EN, isosceles trapezoid)
Therefore the length of KE is 8.
Use pythagoras theorem is triangle EKM.
Therefore the length of side KM is units.
