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}}}.

the area of triangle is:

use Pythagorean theorem to calculate {{{x}}}:

{{{(5x)^2=(x+2)^2+(x+2)^2}}}

{{{25x^2=x^2 + 4x + 4+x^2 + 4x + 4}}}

{{{25x^2=2x^2 + 8x + 8}}}

{{{25x^2-2x^2 - 8x -8=0}}}

{{{23x^2 - 8x -8=0}}}.......use quadratic formula

{{{x = (-(-8) +- sqrt((-8)^2-4*23*(-8) ))/(2*23) }}}

{{{x = (8 +- sqrt(64+736 ))/46 }}}

{{{x = (8 +- sqrt(800 ))/46 }}}

 {{{x = (8 +- 20sqrt(2))/46 }}}.........simplify

{{{x = (4 +-10sqrt(2))/23 }}}

solutions:


{{{x = 4/23 - (10 sqrt(2))/23=-0.44}}}-> disregard negative solution
  
{{{x = 4/23 + (10 sqrt(2))/23=0.79}}}


sides are {{{(0.79+2)}}}m= {{{(2.79)}}}m=>height=base

hypotenuse is {{{5*0.79 }}m={{{3.95 }}}m 



{{{A=(1/2)base*height}}}

{{{A=(1/2)(2.79m)*(2.79m)}}}

{{{A=(1/2)(7.78m^2)}}}

{{{A=3.89m^2)}}}