Question 74

The area of isosceles trapezium is 176 $$cm^{2}$$ and the height h is$$ \frac{2}{11}$$ th of the sum of its parallel sides if the ratio of the length of the parallel sides is 4:7, then the length of a diagonal {in cm) is

Solution

Area =12(sum of parallel sides)× distance between them

12(7x+4x)×2x=176

11x2=176x216

x=4

AB=7×4=28cm

CD=4×4=16cm

CM=2×4=8cm

AM=AN+NM

AN+16

6+16=22

(AN=BM > =12/2=6)

AC^2=CM^2+AM^2

AC^2=8^2+22^2

AC= √ (64+484)------- √(548)...= 2√(137)

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