Answer:
Step-by-step explanation:
x + (x + 2) + (x+4) =12
3x + 6 = 12
3x = 6
x = 2
From the information given you have:
1) Smaller diagonal of the kite: 16 inches
2) Larger diagonal of the kite: height of one triangle (h1) + height of the other triangle (h2)
3) Calculation of the height of the smaller triangle, h1:
10^2 = (16/2)^2 + (h1)^2 => h1 = √ [10^2 - 8^2] = 6
4) Calculation of the height of the larger triangle, h2
17^2 = (16/2)^2 + (h2)^2 => h2 = √[17^2 - 8^2] = 15
5) Larger diagonal = h1 + h2 = 6 + 15 = 21
Answer: 21 inches
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
Answer:
True
Step-by-step explanation:
Adding -ed to a verb will make it a simple past tense verb
Hope this helps :)
Answer:
X = 3
Step-by-step explanation:
