According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, the maximum length of the third side can be 16 cm (7 + 10 - 1). Hence, the answer is 17 cm.

According to the triangle inequality theorem, the length of the third side must be less than the sum of the other two sides and greater than the difference of the two sides. Therefore, the range is 3 cm to 17 cm.

According to the triangle inequality theorem, the length of the third side must be less than the sum and greater than the difference of the other two sides. Therefore, the third side must be greater than 3 cm and less than 17 cm.

The diameter of a circle is indeed twice the radius, making this statement true.

The sum of the interior angles of a polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides. Therefore, as the number of sides increases, the sum of the interior angles also increases.

Using the property that the sum of angles in a triangle is 180 degrees, angle C can be calculated as 180 - (30 + 60) = 90 degrees.

Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.

Since two angles are equal (45 degrees each), triangle DEF is an isosceles triangle.

Using the Pythagorean theorem, hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Using the Pythagorean theorem, since 10^2 = 8^2 + 6^2 (100 = 64 + 36), triangle XYZ is a right triangle.

To find the length of side XZ when two sides and the included angle are known, the Cosine rule is applicable.

Since all sides are of different lengths, triangle XYZ is a scalene triangle.

Using the Pythagorean theorem, since 5^2 + 12^2 = 25 + 144 = 169 = 13^2, triangle XYZ is a right triangle.

Since all sides are of different lengths, triangle XYZ is a scalene triangle.

The longest side in triangle XYZ is XZ, which measures 10 cm.

Area = base × height. Thus, 120 = 15 × height, giving height = 120/15 = 8 m.

Area = base × height. Thus, 120 = 15 × height, giving height = 120/15 = 8 units.

Area = (1/2) × d1 × d2. Thus, 48 = (1/2) × 8 × d2, giving d2 = 12 cm.

Area = (1/2) × d1 × d2. Thus, 60 = (1/2) × 10 × d2, giving d2 = 12 cm.

Area = (1/2) × d1 × d2. Thus, 60 = (1/2) × 10 × d2, giving d2 = 60/(5) = 12 cm.

Area of sector = (θ/360) × πr². Thus, 30 = (θ/360) × 3.14 × 25. Solving gives θ = (30 × 360) / (3.14 × 25) ≈ 72 degrees.

The area of a circle is given by A = πr². Thus, A = π(7)² = 49π ≈ 154 cm².

The area can be calculated as length × width = 4 × 3 = 12 square units.

The area of a regular pentagon can be calculated using the formula (1/4)√(5(5 + 2√5)) * s². For s = 6, the area is approximately 15√5.

Area of a rhombus = (1/2) × d1 × d2 = (1/2) × 10 × 24 = 120 cm².

The area of a triangle is given by (1/2) * base * height. Here, base = 4 and height = 3, so area = (1/2) * 4 * 3 = 6.

The area of a triangle is given by the formula (1/2) * base * height. Thus, Area = (1/2) * 10 * 5 = 25 cm².

Using the distance formula, d = √[(x2 - x1)² + (y2 - y1)²] = √[(4 - 1)² + (5 - 1)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.

Using the distance formula d = √((x2 - x1)² + (y2 - y1)²), we find d = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

Using the distance formula, d = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5.