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:
Each side of the photocopy of the picture is enlarged by a factor of 2 so it would be A.
Step-by-step explanation:
<span>The Complete pattern is 85,700, 8,570, 857, 85.7, 8.57, 0.857.It is nothing but just moving the decimal places to the right side.Otherwise each number should multiplied and divided by 10 so that we derived the complete pattern.When you multiply by moving the decimal point to the right, you also need to add a zero to the end of it. This is an alternative method for the pattern.</span>
Answer:
1/3 is your answer
Step-by-step explanation:
hcjiiii suck
Hi Vance :)
a=leg unknow
b=leg
c=hypotenuse
a²+b²=c²
a²=c²-b²
a²=145² - 144²
a²=21,025 - 20,736
a²=289
a=√289
a=17
unknow leg = 17 units
