Question

find the length of a diagonal of a quadrilateral whose area is 195msquare and the lengths of the perpendiculars to the diagonal from opposite vertics are 8.5m and 11m respectively

Answer 1

AC = 20 m


hope this helps

Answer 2

The length of the diagonal is 20 m.

• Given the diagonal is AC and the perpendicular from B to AC intersects at M  and the perpendicular from D to AC intersects at N.
• Now it is given that Area of quadrilateral ABCD is 195 sq. m
• The lengths of the perpendicular from opposite vertices of the diagonal to the diagonal is given as 8.5m and 11m.
• Let say, BM = 8.5 m and DN = 11 m.
• Now we write ,

• Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ADC

Area of quadrilateral ABCD = (1/2)×AC×BM + (1/2)×AC×DN

195 = (1/2)×AC×BM + (1/2)×AC×DN

195×2 = AC×BM + AC×DN

195×2 = AC×8.5 + AC×11

390 = AC (8.5 + 11)

390 = AC (19.5)

AC = 20 m

• The length of the diagonal is 20 m.