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
<h3>
Answer:</h3>
y - 2
<h3>
Step-by-step explanation:</h3>
You get 2 less than a value when you subtract 2 from that value.
(x+6)2+(y-10)2=36 , would be your equation.
I believe you meant f(x) = x^2 - 3x - 10.
f(b) - f(a)
The ave. r. of c. formula is a. r. c = -----------------
b -a
(6)^2 - 3(6) - 10 - [(4)^2 - 3(4) - 10]
Here, a. r. c. = ------------------------------------------------------
6-4
36 - 18 -10 - 16 + 12 + 10
... which comes out to ---------------------------------------
2
a. r. c. = 7 for x^2 - 3x - 10 on the interval [4,6]
Answer:
0.875
Step-by-step explanation: