The lengths of two adjacent sides of a parallelogram are 17cm and 12cm

1.	The lengths of two adjacent sides of a parallelogram are 17cm and 12cm. One of its diagonal is25cm long. Find the area of the parallelogram. Also find the length of the altitude from vertex onthe side of length 12cm.
Answer» For△BCD: Let a = 17 cm, b = 12 cm, c = 25 cm So its semi-perimeter, s = (a+ b + c)/2 = (17 + 12 + 25)/2 = 27 cm ∴ Area of△BCD = root under(√(s -a)(s - b)(s - c)) = root under(√27(27 - 17)(27 - 12)(27 - 25)) = root under(√27 x 10 x 15 x 2) = 90 cm2 Now, area of parallelogram ABCD = 2 x Area of△BCD = 2 x 90 = 180 cm2 Also, area of parallelogram ABCD = DC x AE ∴180 = 12 x AE ⇒AE = 180/12 = 15 cm

The lengths of two adjacent sides of a parallelogram are 17cm and 12cm. One of its diagonal is25cm long. Find the area of the parallelogram. Also find the length of the altitude from vertex onthe side of length 12cm.

Answer»

For△BCD:

Let a = 17 cm, b = 12 cm, c = 25 cm

So its semi-perimeter, s = (a+ b + c)/2 = (17 + 12 + 25)/2 = 27 cm

∴ Area of△BCD = root under(√(s -a)(s - b)(s - c))

= root under(√27(27 - 17)(27 - 12)(27 - 25))

= root under(√27 x 10 x 15 x 2) = 90 cm2

Now, area of parallelogram ABCD = 2 x Area of△BCD

= 2 x 90 = 180 cm2

Also, area of parallelogram ABCD = DC x AE

∴180 = 12 x AE

⇒AE = 180/12 = 15 cm