A trapezium has an area of 180\text{ cm}^2 and a perpendicular height of 12\text{ cm}. If … — JAMB UTME

A trapezium has an area of $180\text{ cm}^2$ and a perpendicular height of $12\text{ cm}$ . If the lengths of its two parallel sides are in the ratio $2:3$ , calculate the length, in $\text{cm}$ , of the longer parallel side.

Cevap: 18 cm

Cevap

The length of the longer parallel side is

18\text{ cm}

By representing the parallel sides as

2x

and

3x

, the trapezium area formula

A = \frac{1}{2}(a + b)h

gives

180 = \frac{1}{2}(2x + 3x)(12) = 30x

. Solving for

x

yields

x = 6

. Therefore, the longer parallel side is

3(6) = 18\text{ cm}

Adım Adım Çözüm

Express the parallel sides algebraically from the ratio

2:3

Let the shorter parallel side

a = 2x

and the longer parallel side

b = 3x

Using a common multiplier

x

preserves the given side ratio.

Substitute the expressions and known values into the trapezium area formula.

180 = \frac{1}{2}(2x + 3x) \times 12

The area

A

of a trapezium is given by

A = \frac{1}{2}(a + b)h

Solve for the variable

x

180 = 6 \times 5x \implies 30x = 180 \implies x = 6

Simplifying

\frac{1}{2} \times 12 = 6

and multiplying by

(2x + 3x) = 5x

Calculate the length of the longer parallel side.

Longer side

= 3x = 3 \times 6 = 18\text{ cm}

The longer side corresponds to the

3x

term in the ratio.

Anahtar Kavram

Area of a trapezium involving algebraic ratio problem solving

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