Question

the area of a trapezium is 768 cm square .Its altitude is 16cm and one of the parallel side is 10 cm longer than the other . find the length of the sides

Answer 1

given ,

area of trapezium = 768 cm^2

area of trapezium = 1/2( sum of parallel sides )×h

so ;
1/2 (10+x) × 16 = 768 cm^2

8 (10+ x) = 768 cm^2

80 + 8x = 768 cm^2

8x = 768 - 80

8x = 688
x = 688/8
x = 86 cm

Answer 2

Given, Area of Trapezium = 768 ${cm}^2$

Given, Altitude or height of Trapezium = 16 cm

Let the length of one of its parallel side be x

Then other parallel side will be 10 + x

As we know that --
$area \: of \: trapezium \: = \frac{1}{2} (sum \: of \: its \: parallel \: sides)height \\ \\ therefore \\ \\ \frac{1}{2} (x + 10 + x)16 = 768 \\ \\ \frac{1}{2} (2x + 10) 16 = 768 \\ \\ 1(2x + 10)8 = 768 \\ \\ (2x + 10)8 = 768 \\ \\ 16x + 80 = 768 \\ \\ 16x = 768 - 80 \\ \\ 16x = 688 \\ \\ x = \frac{688}{16} \\ \\ x = 43$

Now, x = 43cm

So length of 1 parallel side = 43cm

Length of other parallel side = 10+43 = 53cm