The median has the property of being equal to 1/2 the length of the 2 parallel lines in a trapezoid. In this case. 1/2 [(x + 8) + (5x + 4)] = 24 There is your equation. Now all you have to do is solve it.
1/2 (x + 8 + 5x + 4) = 24 I've removed the inner brackets.
1/2 (6x + 12) = 24 Gathered like terms.
(6x + 12) = 24*2 Multiplied both sides by 2
6x + 12 = 48 removed the brackets.
6x = 48 - 12 subtracted 12 from both sides.
6x = 36 Divide by 6
x = 36/6
x = 6
6 <<< answer.
X+2y=10
6x+6y=6 -> x+y=1
(x+2y=10)-(x+y=1)=y=9
x+(2*9)=10
x+18=10
x=-8 and y=9 -> c
I hope this is what you were looking for.
If we draw a rhombus OABC on a coordinate grid with one vertex at the point O (0,0)
and let its height be 1 then (using the Pythagoras theorem) the coordinates of the 4 points will be as follows:-
O = (0,0) , A = (1, 1), B = (sqrt2+ 1 , 1) , C = (sqrt2, 0)
Slope of the diagonal OB = 1 / (sqrt2 + 1)
Slope of the other diagonal AC = - 1 / (sqrt2 - 1)
Product of the slopes = - 1 / ( sqrt2 + 1)(sqrt2 - 1) = -1 / 1 = -1
This proves that the diagonals are perpendicular.
