You can focus on the two sub-triangles ABC and ACD
We know that they are both right triangles, because we're given that AC and BD are perpendicular.
The sides AB and AD are the hypothenuses of these triangles, so we know their length through the pythagorean theorem:
But since we're given , the expressions for AD and AB are actually the same expression. This proves that AD=AB, and thus that the triangle is isosceles.
Answer:
300
Step-by-step explanation:
305
Question Continuation:
if (a) the books can be arranged in any order?
(b) the mathematics books must be together and the novels must be together?
Answer:
(a) 3628800 ways
(b) 17280 ways
Step-by-step explanation:
Given
Solving (a): In any order
This implies that there is no restriction and the novels, mathematics and biology book are just seen as books.
Total number of books is:
The number of arrangement is:
(b):
If the mathematics books are together, there are 4! different arrangements
If the novels are together, there are 5! different arrangements
Now, there are 3 bundles.
This can be arranged in 3! ways.
Total number of arrangement is: