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

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Solution

The correct option is C
75

Let the length of CD be x cm.

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

[Area of trapezium is half the product of the parallel sides and the distance between them.]

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

(50 + x) x 18 = 2250

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

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

50 + x = 125

x = 125 - 50

x = 75

The length of CD is 75 cm.

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

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