Question

The area of a trapezium is 300 m. The perpendicular distance between the two parallel sides is 15 m. If the difference of the parallel side is 16 m, find the length of the parallel sides.

Answer 1

Question :

• The area of a trapezium is 300 m².

• The perpendicular distance between the two parallel sides is 15 m.

• If the difference of the parallel side is 16 m

• find the length of the parallel sides.

To Find :

• The length of the parallel sides

Let us assume :

The length of the parallel side be x

The other be x + 16 m

Formula Used :

Area of Trapezium = 1/2(a + b)h

Given Data :

Area of the Trapezium is 300 m²

The perpendicular distance between two parallel sides is 15 m

Difference of these parallel sides is 16 m

Solution :

Using the formula we get

Area of trapezium = 1/2(a + b)h

Here, a and b means the parallel sides

Putting the values we get :

300 m² = 1/2(x + x + 16 m)15 m

300 m² = 15/2 m(2x + 16 m)

Transposing 15/2 m on the left hand side of the equation we get

300 m² × 2/15 m = 2x + 16 m

40 m = 2x + 16 m

Again, transposing 16 m on the left hand side we get

40 m - 16 m = 2x

2x = 24 m

x = 24/2 m

x = 12 m

Then the two parallel sides are :

x = 12 m

• So, one side is 12 m

x + 16 m = 12 m + 16 m → 28 m

• So the other side is 28 m

Regards

# BeBrainly

Answer 2

Step-by-step explanation:

Given:

• Area of a trapezium is 300 m.
• The perpendicular distance between the two parallel sides is 15 m.
• If the difference of the parallel sides is 16 m.

To find:

• Length of the parallel sides.

Solution:

Let one of the length of the parallel side be x cm.

Then the other parallel side's length will be x + 16 cm.

∵ The difference of the parallel sides is 16 m.

We know,

Area of a trapezium :

• 1/2 (a + b) h

Where we have,

• a = First parallel side
• b = Second parallel side
• h = Perpendicular distance

Substituting we get,

⇒ 300 = 1/2 (x + x + 16) (15)

⇒ 300 = 15/2 (2x + 16)

⇒ 300 × 2 = 15(2x + 16)

⇒ 600 = 15(2x + 16)

⇒ 600 = 30x + 240

⇒ 600 - 240 = 30x

⇒ 360 = 30x

⇒ x = 360/30

⇒ x = 12

Now, the length of the parallel sides (a and b),

• First side (x) = 12 cm
• Second side (x + 16) = 28 cm

Verification:

Area of trapezium:

• 1/2 (a + b) h

Substituting we get,

⇒ 300 = 1/2(12 + 28) × 15

⇒ 300 = 1/2(40) × 15

⇒ 300 = 20 × 15

⇒ 300 = 300

∴ L.H.S = R.H.S

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