The area of a trapezium is 1586 `cm^2` and the perpendicular distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm, the other side is equal to:

Options

A. 74 cm
B. 76 cm
C. 38 cm
D. 37 cm

Answer

To find the length of the other parallel side of the trapezium, we can use the formula for the area of a trapezium:

\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]

where \( b_1 \) and \( b_2 \) are the lengths of the parallel sides, and \( h \) is the height (the perpendicular distance between the parallel sides).

Given:
- Area = 1586 cm²
- Height (h) = 26 cm
- One parallel side (b1) = 84 cm
- Let the other parallel side (b2) = x cm

### Step 1: Substitute the known values into the area formula

\[ 1586 = \frac{1}{2} \times (84 + x) \times 26 \]

### Step 2: Simplify the equation

First, we can multiply both sides by 2 to eliminate the fraction:

\[ 3172 = (84 + x) \times 26 \]

### Step 3: Divide both sides by 26

\[ \frac{3172}{26} = 84 + x \]

Calculating the left side:

\[ 122 = 84 + x \]

### Step 4: Solve for x

Now, subtract 84 from both sides:

\[ x = 122 - 84 \]

Calculating the right side:

\[ x = 38 \]

### Conclusion

The length of the other parallel side is 38 cm.

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