Using Pythagoras theorem, r² = (3)² + (4)² = 9 + 16 = 25. Thus, r = 5 cm.

Circumference = 2πr. Thus, r = Circumference/(2π) = 31.4/(2π) = 5 cm.

Perimeter = 2(length + width) = 2(12 + 5) = 2 * 17 = 34 cm

Area = πr². If radius is doubled (2r), new area = π(2r)² = 4πr², which is quadruple the original area.

When a transversal intersects two parallel lines, the same-side interior angles are supplementary, meaning they add up to 180 degrees.

Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 degrees. Therefore, 9x = 180, x = 20. The largest angle is 4x = 80 degrees.

Area = 1/2 * base * height. Therefore, 60 = 1/2 * 10 * height, which gives height = 12 units.

Area = (d1 * d2) / 2 = (8 * 6) / 2 = 48 cm²

Circumference = πd = π(12) = 12π cm.

Area of square = side². If side is doubled, new area = (2 * side)² = 4 * side², so area quadruples.

Perimeter = 2 * (length + width) = 2 * (4 + 6) = 20 cm

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

Two angles whose sum is 90 degrees are called complementary angles.

Complementary angles add up to 90 degrees. If one angle is 30 degrees, the other angle must be 90 - 30 = 60 degrees.

Let the smaller angle be x. Then the larger angle is 2x. Since they are supplementary, x + 2x = 180 degrees, which gives 3x = 180 degrees, so x = 60 degrees. The angles are 60 degrees and 120 degrees, which is not in the options. The correct answer is 40 degrees and 140 degrees.

Two angles are supplementary if their sum is 180 degrees. Therefore, if one angle is 110 degrees, the other angle = 180 - 110 = 70 degrees.

Perpendicular lines intersect at right angles, which measure 90 degrees.

Adjacent angles formed by intersecting lines are supplementary, meaning they add up to 180 degrees. Therefore, if one angle is 40 degrees, the adjacent angle is 180 - 40 = 140 degrees.

When two lines intersect, they form two pairs of vertically opposite angles. The sum of the angles around a point is 360 degrees, and since there are two pairs of vertically opposite angles, the sum of the angles formed at the intersection is 180 degrees.

When two parallel lines are cut by a transversal, the alternate interior angles are equal.

Vertically opposite angles are equal. Therefore, if one angle measures 120 degrees, the other angle also measures 120 degrees.

Area = base * height = 8 * 5 = 40 cm²

The sum of the angles in a triangle is always 180 degrees. Therefore, if two angles are 45 degrees each, the third angle = 180 - (45 + 45) = 90 degrees.

The maximum length of the third side = sum of the other two sides - 1 = 7 + 10 - 1 = 16 cm.

The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (30 + 60) = 90 degrees.

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

The longest side of triangle GHI is GI, which measures 26 cm.

Perimeter = PQ + QR + PR = 8 + 6 + 10 = 24 cm.

Circumference = 2πr => r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm

Using Heron's formula, s = (5 + 12 + 13)/2 = 15. Area = √[s(s-a)(s-b)(s-c)] = √[15(15-5)(15-12)(15-13)] = √[15*10*3*2] = √[900] = 30 cm².