The lengths of the parallel sides of a trapezium are (x + 8) cm and (2x + 3) cm, and the distance between them is (x + 4) cm. If its area is 590 cm², find the value of x.
Quadratic Equations
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The lengths of the parallel sides of a trapezium are (x + 8) cm and (2x + 3) cm, and the distance between them is (x + 4) cm. If its area is 590 cm2, find the value of x.

KnowledgeBoat · Accepted Answer

Given, Length of parallel sides of trapezium = (x + 8) cm and (2x + 3) cm. The distance between the parallel lines (height) = (x + 4) cm. Area of trapezium = 590 cm2 By formula, Area of trapezium = × (sum of parallel sides) × height ⇒ 590 = (x + 8 + 2x + 3)(x + 4) ⇒ 590 × 2 = (3x + 11)(x + 4) ⇒ 1180 = 3x2 + 12x + 11x + 44 ⇒ 1180 = 3x2 + 23x + 44 ⇒ 0 = 3x2 + 23x + 44 - 1180 ⇒ 3x2 + 23x - 1136 = 0 ⇒ 3x2 - 48x + 71x - 1136 = 0 ⇒ 3x(x - 16) + 71(x - 16) = 0 ⇒ (3x + 71)(x - 16) = 0 ⇒ (x - 16) = 0 or (3x + 71) = 0 [Using zero-product rule] ⇒ x = 16 or x = Since, length cannot be negative. Thus, x = 16 Hence, value of x = 16.

Mathematics

The lengths of the parallel sides of a trapezium are (x + 8) cm and (2x + 3) cm, and the distance between them is (x + 4) cm. If its area is 590 cm², find the value of x.

Quadratic Equations

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