Question

Q.1 The length of two adjacent sides of parallelogram are 17cm and 12 cm. One of its diagonals is 25cm long. Find the area of the parallelogram, also find the altitude from vertex on the side of length 12cm. Please help

Answer 1

Please read last 2 lines.

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 .