The cross-section of a trough of depth 36 cm is a trapezium ABCD where AB = 50 cm as shown. If the area of ABCD is 2250 $c m^{2}$ , find the length of CD in cm.

25 cm

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50 cm

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75 cm

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100 cm

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Solution

The correct option is C
75 cm

Let the length of CD be x cm.

Area of ABCD = $\frac{1}{2}$ x (AB +CD) x depth

$\frac{1}{2}$ x (50 + x) x 36 = 2250

50 + x = $\frac{2250}{18}$

50 + x = $\frac{2250}{18}$

50 + x = 125

x = 75

The length of CD is 75 cm.

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The cross-section of a trough of depth 36 cm is a trapezium ABCD where AB = 50 cm as shown. If the area of ABCD is 2250 cm2, find the length of CD in cm.

The correct option is C 75 cm Let the length of CD be x cm. Area of ABCD = 12 x (AB +CD) x depth 12 x (50 + x) x 36 = 2250 50 + x = 225018 50 + x = 225018 50 + x = 125 x = 75 The length of CD is 75 cm.

The cross-section of a trough of depth 36 cm is a trapezium ABCD where AB = 50 cm as shown. If the area of ABCD is 2250 $c m^{2}$ , find the length of CD in cm.

The correct option is C
75 cm

Let the length of CD be x cm.

Area of ABCD = $\frac{1}{2}$ x (AB +CD) x depth

$\frac{1}{2}$ x (50 + x) x 36 = 2250

50 + x = $\frac{2250}{18}$

50 + x = $\frac{2250}{18}$

50 + x = 125

x = 75

The length of CD is 75 cm.