The radius r is half of the diameter, so r = 12/2 = 6 cm. The area A = πr² = π(6)² = 36π cm².

The radius r = diameter/2 = 14/2 = 7 cm. The area A = πr² = π(7)² = 49π ≈ 154 cm².

The circumference C of a circle is given by C = πd. Here, d = 14 cm, so C = π * 14 ≈ 43.98 cm, which rounds to 44 cm.

The circumference C of a circle is given by C = πd. Thus, C = π(14) ≈ 44 cm.

Circumference = πd = (22/7) * 14 = 44 cm.

The radius is half of the diameter. Therefore, the radius is 14/2 = 7 cm.

Radius = diameter/2 = 20/2 = 10 cm.

The nth term of a geometric progression is given by a_n = a * r^(n-1). Here, a = 3, r = 2, and n = 4. So, a_4 = 3 * 2^(4-1) = 3 * 2^3 = 3 * 8 = 24.

The nth term of a geometric progression is given by a_n = a * r^(n-1). Here, a = 5, r = 3, and n = 3. So, a_3 = 5 * 3^(3-1) = 5 * 3^2 = 5 * 9 = 45.

The nth term of a geometric sequence is a * r^(n-1). Here, a = 3, r = 2, n = 4. So, 3 * 2^(4-1) = 3 * 8 = 24.

The nth term of an AP is given by a_n = a + (n-1)d. Here, a = 4, d = 5, and n = 10. So, a_10 = 4 + (10-1)5 = 4 + 45 = 49.

Perimeter = 3 + 4 + 5 = 12 cm.

Since 5² + 12² = 13², it is a right triangle.

Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √(s(s-a)(s-b)(s-c)) = √(28(28-7)(28-24)(28-25)) = √(28*21*4*3) = 84 cm².

Perimeter = 7 + 24 + 25 = 56 cm.

Perimeter = 7 + 24 + 25 = 56 cm.

Let the sides be 3x, 4x, 5x. Then, 3x + 4x + 5x = 60. Therefore, 12x = 60, x = 5. Longest side = 5x = 25 cm.

Triangle ABC is a right triangle because it satisfies the Pythagorean theorem: 3² + 4² = 5².

Yes, because 7² + 24² = 49 + 576 = 625 = 25², satisfying the Pythagorean theorem.

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, perimeter = 7 + 24 + 25 = 56 cm.

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

Yes, because 8^2 + 15^2 = 64 + 225 = 289 = 17^2, satisfying the Pythagorean theorem.

Area = 1/2 * side1 * side2 = 1/2 * 5 * 12 = 30 cm².

According to the triangle inequality theorem, the length of the third side must be less than the sum of the other two sides. Therefore, the maximum length is 5 + 12 = 17 cm.

The length of the third side must be greater than the difference of the other two sides and less than their sum: |5 - 12| < third side < 5 + 12, which gives 7 cm < third side < 17 cm.

The length of the third side must be greater than the difference of the other two sides and less than their sum: |5 - 7| < third side < 5 + 7, which gives 2 < third side < 12.

The length of the third side must be greater than the difference of the other two sides and less than their sum: |6 - 8| < third side < 6 + 8, which gives 2 cm < third side < 14 cm.

Area = 1/2 * a * b * sin(C) = 1/2 * 8 * 15 * sin(60) = 60 cm².

The length of the third side must be greater than the difference of the other two sides and less than their sum: |8 - 6| < third side < 8 + 6, which gives 2 < third side < 14.