The area of a field is in the shape of a trapezium measures $1440 m^{2}$ . The perpendicular distance between its parallel sides is $24 m$ . If the ratio of the parallel sides is $5 : 3$ . What is the length of the longer parallel side?

75 m

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70 m

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80 m

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85 m

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Solution

The correct option is A $75 m$
Let sides of the field are $5 x$ and $3 x$ .
Area of field $= \frac{s i d e_{1} + s i d e_{2}}{2} \times h$
Area of field $= \frac{1}{2} \times (5 x + 3 x) \times 24$
$= 96 x m^{2}$
$\Rightarrow 96 x = 1440$
$\Rightarrow x = \frac{1440}{96} = 15 m$
Therefore, length of longer parallel side $= 15 \times 5 = 75 m$

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The area of a field is in the shape of a trapezium measures 1440m2. The perpendicular distance between its parallel sides is 24m. If the ratio of the parallel sides is 5:3. What is the length of the longer parallel side?

The correct option is A 75mLet sides of the field are 5x and 3x.Area of field =side1+side22×hArea of field=12×(5x+3x)×24=96x m2⇒96x=1440⇒x=144096=15mTherefore, length of longer parallel side=15×5=75m

The area of a field is in the shape of a trapezium measures $1440 m^{2}$ . The perpendicular distance between its parallel sides is $24 m$ . If the ratio of the parallel sides is $5 : 3$ . What is the length of the longer parallel side?