In the diagram, AC=BD. Show that AB=CD
1 answer:
You might be interested in
<em><u>Statement:</u></em>
The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.
<em><u>To find out:</u></em>
The length of the larger side of the right angled triangle.
<em><u>Solution:</u></em>
Let us consider x as the smaller side and y as the larger side.
Then, in the right angled triangle,
x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]
Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).
And if the larger side is increased by 3 cm, then the larger side will be (y + 3).
Then, in the new right angled triangle,
(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]
or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²
or, x² + 4x + 4 + y² + 6y + 9 = (√117)²
or, x² + y² + 4x + 6y + 13 = (√117)²
Now, put the value of x² + y² from equation (I),
or, (2√13)² + 4x + 6y + 13 = (√117)²
or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)
or, 52 + 4x + 6y + 13 = 117
or, 4x + 6y = 117 - 52 - 13
or, 4x + 6y = 52
or, 4x = 52 - 6y
or, x = ...(II)
Now, put the value of x of equation (II) in (I),
x² + y² = (2√13)²
or, + y² = 52
or, = 52
or, 52y²-624y + 2704 = 52 × 16
or, 52y² - 624y + 2704 - 832 = 0
or, 52y² - 624y + 1872 = 0
or, 52(y² - 12y + 36) = 0
or, y²-12y +36 = 0 ÷ 52
or, y²-12y +36 = 0
or, (y)² - 2 × 6 × y + (6)² = 0
or, (y - 6)² = 0
or, y - 6=0
or, y = 6
We have taken y as the length of the larger side of the right angled triangle.
So, the length of the larger side is 6 cm.
<em><u>Answer:</u></em>
6 cm
Hope you could understand.
If you have any query, feel free to ask.
The question is incomplete. Below you will find the missing contents.
The correct match of events with order are,
- P(A)P(B|A) - Dependent event
- P(A)+P(B) - Mutually exclusive events
- P(A and B)/P(A) - Conditional events
- P(A) . P(B) - Independent Events
- P(A)+P(B) -P(A and B) - not Mutually exclusive events.
When two events A and B are independent then,
P(A and B)=P(A).P(B)
when A and B are dependent events then,
P(A and B) = P(A) . P(B|A)
When two events A and B are mutually exclusive events then,
P(A and B)=0
So, P(A or B) = P(A) + P(B) - P(A and B) = P(A) + P(B)
P(A) + P(B) = P(A or B)
When events are not mutually exclusive then the general relation is,
P(A or B) = P(A) + P(B) - P(A and B)
If the probability of the event B conditioned by A is given by,
Hence the correct match are -
Dependent event
Mutually exclusive events
Conditional events
Independent Events
not Mutually exclusive events.
Learn more about Probability of Events here -
#SPJ10
