If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore
ΔABC is similar to ΔADE.
The sides of smaller triangle are in proportion with sides of bigger triangle.
Therefore we have the equation:

We have AC = x, AE = x + 15, AB = 8, AD = 8 + 10 = 18.
Substitute:
<em>cross multiply</em>
<em>use distributive property a(b + c) = ab + ac</em>
<em>subtract 8x from both sides</em>
<em>divide both sides by 10</em>

<h2>Answer: AC = 12</h2>
Answer:
572
Step-by-step explanation:
Work :
Answer:
The area of the rectangle is increasing at a rate of
.
Step-by-step explanation:
Given : The width of a rectangle is increasing at a rate of 2 cm/ sec. While the length increases at 3 cm/sec.
To find : At what rate is the area increasing when w = 4 cm and I = 5 cm?
Solution :
The area of the rectangle with length 'l' and width 'w' is given by 
Derivative w.r.t 't',

Now, we have given




Substitute all the values,



Therefore, the area of the rectangle is increasing at a rate of
.
The number 2+√3 is irrational ,it cannot be expressed as a ratio of integers a and b. To prove that this statement is true, let us Assume that it is rational and then prove it isn't (Contradiction).
So the Assumptions states that :
(1) 2+√3
Where a and b are 2 integers
Now since we want to disapprove our assumption in order to get our desired result, we must show that there are no such two integers.
Squaring both sides give :
3=a/b
3=a^2/ b^2
what two number time itself (twice) can be divide by another number time itself (twice) to get 3