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Alex73 [517]
2 years ago
11

Find the length of the third side. If necessary, round to the nearest tenth. 25 20 ​

Mathematics
1 answer:
Komok [63]2 years ago
3 0

Answer:

15

Step-by-step explanation:

using \: pythagoras \: theorem \\ let \: the \: unknown \: side = x \\ 25 {}^{2}  = x {}^{2}  + 20 {}^{2}  \\ 625 = x {}^{2}  + 400 \\ x {}^{2}  = 625 - 400 \\ x {}^{2}  { = 225} \\ x =  \sqrt{225}   \\ x = 15 \\ lenght \: of \: the \: third \: side = 15

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In triangle abc, the perimeter is 36, and ab=ac. line ad is perpendicular to bc at the point d, and triangle abd's perimeter is
Musya8 [376]
Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

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The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

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(eq.2) 2x + y + 2z = 60

Substitute 2x + y by 36 from (eq.1) in (eq.2):

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The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

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ad = 30 - (36/2) = 30 - 18 = 12
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3 years ago
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