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(i) A rectangle has a length of 15 cm and width of 10 cm. If the length is increased by 20% and the width is decreased by 10%, the new area of the rectangle is P cm2.
(ii) A right-angled triangle has legs of lengths 6 cm and 8 cm. The length of the hypotenuse is Q cm.
Fill in the blanks and select the correct option.
(i) The sum of the interior angles of a polygon with 10 sides is P degrees.
(ii) The area of a square is 144 cm². The length of its diagonal is Q cm.
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(i) The number of diagonals in a hexagon is P.
(ii) The length of each side of an equilateral triangle with an area of 9√3 cm2 is Q cm.
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(i) The surface area of a sphere with radius 7 cm is P cm2.
(ii) The volume of a cube with side 5 cm is Q cm3.
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(i) The sum of the first 20 natural numbers is P.
(ii) The sum of the squares of the first 10 natural numbers is Q.
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(i) The perimeter of a rectangle is 54 cm. If its length is 16 cm, its width is P cm.
(ii) The circumference of a circle with a radius of 7 cm is Q cm.
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(i) The value of P if (x - 2)(x - 3) = x2 - Px + 6.
(ii) The value of Q if the mean of the first 5 prime numbers is Q.
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(i) The area of a trapezium with bases 10 cm and 6 cm, and height 5 cm is P cm2.
(ii) The area of a triangle with base 8 cm and height 12 cm is Q cm2.
Fill in the blanks and select the correct option.
(i) If the quadratic equation x2 - 7x + 10 = 0 has roots α and β, then the value of α + β is P.
(ii) If the arithmetic mean of 8, 10, 12, 14, and 16 is Q.
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(i) The LCM of 12 and 15 is P.
(ii) The HCF of 24 and 36 is Q.