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
2. The absolute value of -8 is 8. True
3. An isosceles triangle has three congruent sides.
Nope. It has two
4. The cosine is the ratio between the length of the opposite leg to the length of the hypotenuse.
I have no idea.
5. The boiling point of water is 212°C.
true
6.
The expression 28xyz has 4 terms.
true
7.
Shapes that have the same size and shape are said to be similar.
false
8.
The points where the sides of a polygon meet are called the vertexes.
true
9. A heptagon is a seven-sided polygon.
true (hexagon)
10.
An acute angle has more than 90° but less than 180°.
true
A. Jim Claire Brenda peter and Micah
B. Jim and Claire
C. no because it would only result in 4 lb and I need 4.25 lb
Answer:
20
Step-by-step explanation:
