Find the exact perimeter of this triangle?
![enter image source here]()
Answer is: 6sqrt2 + 10 units
Answer is:
1 Answer
Jul 12, 2017
Explanation:
"to find the value of x use "color(blue)"Pythagoras' theorem"
"that is" the square on the hypotenuse of a right triangle is equal to the sum of squares on the other two sides.
rArrx^2+(x+3)^2=(x+4)^2
"expand brackets using the FOIL method gives"
x^2+x^2+6x+9=x^2+8x+16
"collect terms on left side and equate to zero"
x^2-2x-7=0larra=1,b=-2,c=-7
"solve using the "color(blue)"quadratic formula"
x=(2+-sqrt(4+28))/2=(2+-sqrt32)/2
color(white)(x)=(2+4sqrt2)/2=1+2sqrt2larr" positive only"
"perimeter "= x+x+3+x+4=3x+7
color(white)(perimeter)=3(1+2sqrt2)+7
color(white)(perimeter)=3+6sqrt2+7
color(white)(perimeter)=6sqrt2+10larr" exact value"
