In a trapezium-shaped field, one of the parallel sides is twice the ot

1.	In a trapezium-shaped field, one of the parallel sides is twice the other. If the area of the field is 9450 m2 and the perpendicular distance between the two parallel sides is 84 m, find the length of the longer of the parallel sides.
Answer» Given Let length of first parallel side X Length of other parallel side is 2X Area of trapezium= 9450 m² Let Height (h) = 84 m We know that area of trapezium is \(\frac{1}{2}\)× (sum of parallel sides) × height Therefore Area of trapezium is \(\frac{1}{2}\)× (X + 2X) × 84 = 9450cm². \(\therefore\) \(\frac{1}{2}\)× (X + 2X) × 84 =9450 ⇒ (3X) × 42 =9450 ⇒ 126X = 9450 ⇒ 2X + 6 = \(\frac{9450}{126}=75\) ⇒ X = 17 ∴ Length of the parallel sides is X = 75 m and 2X = 150 m. Therefore length of the longest is 150 m.

In a trapezium-shaped field, one of the parallel sides is twice the other. If the area of the field is 9450 m2 and the perpendicular distance between the two parallel sides is 84 m, find the length of the longer of the parallel sides.

Answer»

Given

Let length of first parallel side X

Length of other parallel side is 2X

Area of trapezium= 9450 m²

Let Height (h) = 84 m

We know that area of trapezium is \(\frac{1}{2}\)× (sum of parallel sides) × height

Therefore Area of trapezium is \(\frac{1}{2}\)× (X + 2X) × 84 = 9450cm².

\(\therefore\) \(\frac{1}{2}\)× (X + 2X) × 84 =9450

⇒ (3X) × 42 =9450

⇒ 126X = 9450

⇒ 2X + 6 = \(\frac{9450}{126}=75\)

⇒ X = 17

∴ Length of the parallel sides is X = 75 m and 2X = 150 m.

Therefore length of the longest is 150 m.