trapezium with parallel sides in the ratio16: 5 is cut from a rectangle whose sides measure 63 and 5 metre respectively.the area of trapezium is 4/15 of the area of the rectangle.find The length of the parallel sides of the trapezium
Answers
Answer:
Step-by-step explanation:
=> Let ABCD be the rectangle whose sides are 63 and 5 m.
Thus, Area of rectangle = (63 * 5) m²
= 315 m²
=> Let trapezium PQCD is cut from the rectangle.
∴ Height of the trapezium = 5 m
=> Area of trapezium is 4/15 of the area of the rectangle.
Area of trapezium = 4/15 * area of the rectangle
= 4/15 * 315
= 84 m²
=> Ratio of the parallel sides of trapezium is 16: 5.
Thus, the length of the parallel sides are 16x and 5x respectively.
Area of trapezium = ¹/₂ × height × sum of parallel sides
84 m² = ¹/₂ * 5 * (16x + 5x)
168 m² = 80x + 25x
168 m² = 105x
x = 168 / 105
=> Thus, the length of the parallel sides:
16x = 16 * 168/105
= 25.6 m
5x = 5 * 168/105
= 8 m
Hence, The length of the parallel sides of the trapezium are 25.6 m and 8 m respectively.
Answer:Let ABCD be the rectangle whose sides are 63 and 5 m.
Thus, Area of rectangle = (63 × 5) m²
= 315 m²
=> Let trapezium PQCD is cut from the rectangle.
∴ Height of the trapezium = 5 m
=> Area of trapezium is 4/15 of the area of the rectangle.
Area of trapezium = 4/15 × area of the rectangle
= 4/15 × 315
= 84 m²
=> Ratio of the parallel sides of trapezium is 16: 5.
Thus, the length of the parallel sides are 16x and 5x respectively.
Area of trapezium = ¹/₂ × height × sum of parallel sides
84 m² = ¹/₂ × 5 × (16x + 5x)
168 m² = 80x + 25x
168 m² = 105x
x = 168 / 105
=> Thus, the length of the parallel sides:
16x = 16 × 168/105
= 25.6 m
5x = 5 × 168/105
= 8 m
Hence, The length of the parallel sides of the trapezium are 25.6 m and 8 m respectively.