A) A right-angled triangle

Explanation:We are given that the angles of a triangle are in the ratio (1:4:5).
Let’s use this information to determine the type of triangle.
Step 1: Understand the sum of the angles of a triangle
The sum of the interior angles of any triangle is always (180⁰).
Step 2: Let the angles be (x), (4x), and (5x)
Since the angles are in the ratio (1:4:5), we can represent the angles as:
– First angle = (x),
– Second angle = (4x),
– Third angle = (5x).
Step 3: Set up the equation
The sum of the angles in a triangle is 180⁰:
x + 4x + 5x = 180
Step 4: Solve for (x)10x = 180x = = 18
Step 5: Calculate the individual angles
Now that we know (x = 18), we can find the actual angles:
– First angle = (x = 18⁰),
– Second angle = (4x = 4 X 18 = 72⁰),
– Third angle = (5x = 5 X 18 = 90⁰).
Step 6: Identify the type of triangle
Since one of the angles is 90⁰, the triangle is a right triangle.

C) 207

Explanation:To determine the number of times the robin flaps its wings in one and a half minutes, we can use the information given:
– The robin flaps its wings 23 times in 10 seconds.
– We need to find the total flaps in 1.5 minutes (which is 90 seconds).
Step 1: Find the number of flaps per second
First, determine how many times the robin flaps its wings per second:
Flaps per second = = 2.3 flaps per second
Step 2: Find the number of flaps in 90 seconds
Now, multiply the flaps per second by 90 seconds:
Flaps in 90 seconds} = 2.3flaps per second X 90seconds}
= 207flaps

B) 44

Explanation:We are given a triangle with the following information:
– The height of the triangle is double the length of its base.
– The area of the triangle is 484 sq.cm
Step 1: Formula for the area of a triangle
The formula for the area ( A ) of a triangle is:
A =
Step 2: Let the base of the triangle be (b) cm
Since the height is double the base, the height will be ( 2b ) cm.
Substituting these values into the area formula:
484 =
Step 3: Simplify the equation
484 = 484 = b²
Step 4: Solve for ( b )
Taking the square root of both sides:
b = = 22 cm
Step 5: Find the height
Since the height is double the base, the height is:
Height = 2b = 2 X 22 = 44 cm

D) 2000

Explanation:We are asked to simplify the expression:(105)² – (95)²
Step 1: Use the difference of squares formula
The difference of squares formula states:
a² – b² = (a – b)(a + b)
In our case, ( a = 105 ) and ( b = 95 ).
Applying the formula:
(105)² – (95)² = (105 – 95)(105 + 95)
Step 2: Simplify the factors
Now, simplify each part:105 – 95 = 10 and 105 + 95 = 200
Thus, the expression becomes:(105)² – (95)² = 10 X 200 = 2000