Question

The height of trapezium is 68 cm , and the sum of its parallel sides is 75cm. If the area of trapezium is $\frac{6}{17}$ times of the area of square, the the length of diagonal of the square is? (Take $\sqrt{2}=1.41$)

• A. 119.85
• B. 120
• C. 138
• D. 118

Answer 1

Answer:

A. 119.85

height of trapezium is 68 cm

$h=68cm$

sum of its parallel sides is 75cm

$a+b=75cm$

area of trapezium is $\frac{6}{17}$ times of the area of square

Area of trapezium $= \frac{1}{2}\times{h}\times(a+b)$

$\frac{1}{2}\times{68}\times{75}=\frac{6}{17}\times{a^2}$

$a^2=17\times{17}\times{25}$

$a=17\times{5}$

$a=85cm$

Length of diagonal of square $= a\sqrt{2}=85\times{1.41}$

$=119.85cm$