Question

the area of a quadrilateral ABCD is 256 sq. cm. the length of one of its diagonals is 16 cn, tge oeroendicular on this diagonal from the opposite vertices are in the ratio 7:9. find the length of these perpendicular

Answer 1

Here area of quadrilateral given 256 cm²

Let the length of perpendiculars be 7x and 9x (ratio is 7:9)

Length of diagonal = 16 cm

We know that

Area of Quadrilateral = 1/2(sum of perpendiculars on diagonal) × diagonal

∴ 256 = 1/2( 7x + 9x ) × 16

256/16 = (1/2) × 16x

8x = 16

x = 2

∴ Length of perpendiculars

7x = 14 cm and 9x = 18 cm