SOLUTION: A lawn is in the shape of a right angled triangle.The length of two shorter sides are (x+2)m ,while the length of hypotenuse is 5x m.Form and solve an equation in x and hence find

Algebra ->  Length-and-distance -> SOLUTION: A lawn is in the shape of a right angled triangle.The length of two shorter sides are (x+2)m ,while the length of hypotenuse is 5x m.Form and solve an equation in x and hence find      Log On


   

Question 1151651: A lawn is in the shape of a right angled triangle.The length of two shorter sides are (x+2)m ,while the length of hypotenuse is 5x m.Form and solve an equation in x and hence find the area of the lawn in m^2.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A lawn is in the shape of a right angled triangle.
The length of two shorter sides are %28x%2B2%29m ,while the length of hypotenuse is %285x%29m+.
Form and solve an equation in x and hence find the area of the lawn in m%5E2.
the area of triangle is:
use Pythagorean theorem to calculate x:
%285x%29%5E2=%28x%2B2%29%5E2%2B%28x%2B2%29%5E2
25x%5E2=x%5E2+%2B+4x+%2B+4%2Bx%5E2+%2B+4x+%2B+4
25x%5E2=2x%5E2+%2B+8x+%2B+8
25x%5E2-2x%5E2+-+8x+-8=0
23x%5E2+-+8x+-8=0.......use quadratic formula
x+=+%28-%28-8%29+%2B-+sqrt%28%28-8%29%5E2-4%2A23%2A%28-8%29+%29%29%2F%282%2A23%29+
x+=+%288+%2B-+sqrt%2864%2B736+%29%29%2F46+
x+=+%288+%2B-+sqrt%28800+%29%29%2F46+
x+=+%288+%2B-+20sqrt%282%29%29%2F46+.........simplify
x+=+%284+%2B-10sqrt%282%29%29%2F23+
solutions:

x+=+4%2F23+-+%2810+sqrt%282%29%29%2F23=-0.44-> disregard negative solution

x+=+4%2F23+%2B+%2810+sqrt%282%29%29%2F23=0.79

sides are %280.79%2B2%29m= %282.79%29m=>height=base
hypotenuse is 5%2A0.79+%7D%7Dm=%7B%7B%7B3.95+m


A=%281%2F2%29base%2Aheight
A=%281%2F2%29%282.79m%29%2A%282.79m%29
A=%281%2F2%29%287.78m%5E2%29
A=3.89m%5E2%29