Question

Perimeter of quadrilateral is 590 m and its sides are in ratio 5:12:17:25 .find area? first two sides are perpendicular to each other

Answer 1

Answer:

let sides a=5x, b=12x, c=17x, & d=25x

a+b+c+d = 590

5x+12x+17x+25x = 590

59x = 590

x = 590/59 = 10

a=50

b=120

c=170

d=250

First two sides are perpendicular so diagonal of quadrilateral (let diagonal k) by Pythagoras theorem

k² = 50²+120²

= 2500+14400= 16900

k² = 16900 => k = √16900

k = 130 diagonal

Right Angled Triangle ABC in Quadrilateral ABCD

by Herons formula

let a = 50, b = 120 & c = 130

semi permeter s = a+b+c/2

s = 50+120+130/2= 150

∆ = √s(s-a)(s-b)(s-c)

= √150x100x30x20

∆ = 3000

Now in triangle ACD

again let a = 170, b = 250 & c = 130(diagonal of quadrilateral)

s = 170+250+130/2

s = 275

∆ = √275x105x25x145

= 10230.92

Now Area of Quadrilateral ABCD = ABC+ACD

= 3000+10230.92

= 13230.92