Geometry problem?

Question

In the adjacent squares shown, the vertices A,B, and C lie in a straight line. The value of x is: (exact value)
http://www.e-zgeometry.com/pow/pictures/24.gif

Answer 1

treat this as a straight line
graph

A(0,4)=(s1,t1)
B(4,7)=(s2,t2)

equation of line:

t-t1=(t2-t1)(s-s1)/(s2-s1)
t-4=(7-4)(s-0)/(4-0)
t-4=3s/4
t=(3/4)s+4........(1)

AC is a straight line (given)
co-ordinates C=(11,x)
substitute into (1)
t=x=(3/4)*11+4
=33/4+16/4=49/4
=12.25 units
therefore, x=12.25 units

i hope that this helps

Answer 2

x=6.25

This is because if the points lie in a straight line, you can imagine them to lay on a grid. We know that point A has the coordinates of (0,4) and point B has the coordinates of (4,7). When we find the slope of the line running through these points, we get m=3/4. This means that the equation of the line is y=(3/4)x+4. We know the the x-coordinate of point C is 11, because 4+7=11, we can plug 11 into our equation as x, so y=(3/4)(11)+4, giving us y=6.25 This means that x=6.25, because we now know that point C's coordinates are (11,6.25). The height is 6.25 units, and if it's a square, the length, x, is also 6.25 units.

It sounds a little confusing, but you'll get the hang of it.
I hope I was helpful. Good luck!

Answer 3

I tried a different method to stmc but came up with the same answer. My method was trigonometrical. How can the office be correct. How can x be less than 7? I think he has confused himself.

It's just proportionality 7/4=x/7

Therefore

(7*7)/4 = x

stmc's logic is simple and correct give the points to her!

Actually, I've just realised where the office went wrong. He simply did his arithmetic wrong 11*(3/4)+4= 12.25 so he was nearly right!

Answer 4

It is essential to draw the diagram on to paper.
Join AB and draw horizontal thro` A to intersect vertical thro` B at D.
This gives a right angled triangle ABD right angled at D.
Gradient of AB = 3/4.
Similarly draw horizontal thro` B to intersect vertical thro` C at E.
Gradient of BC = 3/4
3/4 = CE/7
CE = 21/4
Length of of vertical side of largest square is then given by
21/4 + 7 = 12 (1/4) = 12.25
Thus x = 12.25

Answer 5

if increase in height of third square is y then by similar triangles
y/3 = 7/4
so y =7/4*3 = 21/4 = 5.25
this now makes the third square x = 7+ 5.25 = 12.25

Answer 6

Yup! grad of line ABC=0.75. So x= 7+5.25=12.25
Know what there going to ask you now?
'What is the length of the nth square in this series?'
Got it? Xn=X1*(1+m)^n-1 where X1=4cm, m=0.75
Go ahead!.. impress teach!

Answer 7

i guess the side are proportional

7/4=x/7

4x=49

x=12.25