Question

The area of a trapezium is 384cm². Its parallel sides are in the ratio 3:5 and the perpendicular distance between them is 12cm. Find the length of each one of the parallel sides its longer side.

Answer 1

Given :-

• The area of a trapezium is 384cm². Its parallel sides are in the ratio 3:5 and the perpendicular distance between them is 12cm.

To find :-

• Length of parallel sides

Solution :-

• Area of trapezium = 384 cm²
• Parallel sides in ratio = 3:5
• Perpendicular distance between parallel sides = 12cm

Let the parallel sides be 3x and 5x

As we have that

→ Area of trapezium = 384

→ ½ × sum of parallel sides × height = 384

→ ½ × (a + b) × h = 384

→ ½ × (3x + 5x) × 12 = 384

→ ½ × 8x × 12 = 384

→ 8x × 6 = 384

→ 48x = 384

→ x = 384/48

→ x = 8

Hence,

• Measures of parallel sides
• First parallel side (smaller) = 3x = 24 cm
• Second parallel side (longer) = 5x = 40cm

Verification :-

• Area of trapezium = 384

→ ½ × (a + b) × h

→ ½ × (24 + 40) × 12

→ ½ × 64 × 12

→ 64 × 6

→ 384 cm²

Hence, verified

Extra Information :-

• Area of circle = πr² where " r " is radius

• Circumference of circle = 2πr

• Perimeter of rectangle = 2(l + b) where " l " is length and " b " is breadth

• Perimeter of square = 4 × a where " a " is side of the square

• Area of rhombus = ½ × product of diagonals

• Area of Parallelogram = b × h where " b " is base and " h " is height

Answer 2

$\bf \to \: \green{{ \underline{given \div }}} \\ \\ \sf \to \: the \: area \: of \: trapezium \: = 384 {cm}^{2} \\ \\ \sf \to \: its \: parallel \: sides \: are \: in \: the \:ratio \: = 3 \ratio 5 \\ \\ \sf \to \: distance \: between \: them \: is \: = 12cm$

$\bf \to \: \orange{{ \underline{to \: find \div }}} \\ \\ \sf \to \:the \: length \: of \: each \: one \: of \: the \: parallel \: sides$

$\bf \to \: { \underline{solution \div }}$

$\sf \to \: area \: of \: trapezium \: = 384cm {}^{2} \\ \\ \sf \to \: its \: parallel \: sides \: = 3 \ratio5 \\ \\ \sf \to \: let \: the \: shorter \: sides \: = 3x \\ \\ \sf \to \: let \: the \: longer \: sides \: = 5x \\ \\ \sf \to \: height \: = 12cm \\ \\ \sf \to \: \blue{{ \underline{formula \: of \: area \: of \: trapezium}}} \\ \\ \sf \to \: \dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times (height) \\ \\ \sf \to \: 384 = \frac{1}{ \cancel{2}} \times (3x + 5x) \times \cancel{12} \\ \\ \sf \to \: 384 = 8x \times 6 \\ \\ \sf \to \: \cancel{384} = 8x \times \cancel{6} \\ \\ \sf \to \: 64 = 8x \\ \\ \sf \to \: x \: = \cancel{ \frac{64}{8} } = 8 \\ \\ \sf \to \: x \: = 8cm \\ \\ \sf \to \: \: \therefore \: length \:of \: shorter \: sides \: = 3x \: = 3 \times 8 = 24cm \\ \\ \sf \to \: length \: of \: longer \: sides \: = 5x = 5 \times 8 = 40cm$