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2 years ago

35 points for this

Mathematics

2 answers:

dusya [7]2 years ago

5 0

Answer:

y = 27.5

Step-by-step explanation:

Because when x=120 and then umps down to 60, thats half of 120

So you just have to divide 55 by 2 and get 27.5 (I doubled checked on a calculator to make sure!!) Hope this helps!!! :D

BabaBlast [244]2 years ago

3 0

Answer:

I think it would be y = 27.5

Step-by-step explanation:

If x = 120 and y = 55, and x=60, or half of 120, then y would be half of 55, or 27.5

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2 years ago

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Step-by-step explanation:

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2 years ago

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2 years ago

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:

Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36

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.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60

So, we have two equations on x, y and z:

(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60

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

(eq.2') 36 + 2z = 60

And solve for z:

36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

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).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

ad = 30 - (36/2) = 30 - 18 = 12

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2 years ago

35 points for this ​

35 points for this