Question

. The area of ​​a quadrilateral farm is 486 m2 and its diagonal is 36 m. Find the length of the vertices of the vertices, if the ratio of the perpendicular to the diagonals placed on the diagonal is 4: 5.​

Answer 1

Area of quadrilateral = 1/2 × diagonal × ( sum of perpendicular on the diagonal )

let the perpendicular be 4x and 5x

486 = 1/2 × 36 × (4x+5x)

486 = 18 × 9x

486-18 = 9x

468/9. = X

X = 52

perpendiculars are 4x = 4 × 52 = 208 m

5x = 5 × 52 = 260 m

Answer 2

Let the perpendicular on the diagonal be as 4x and 5x

area of quad. farm=1/2×36×(4x+5x)

486m square =18×9x

486/18 = 9x

27=9x

x= 27/9=3

therefore,

4x=4×3=12

and

5x= 5×3=15