Question

The figure above shows three squares with sides of length $5$, $7$, and $x$, respectively. If $A$, $B$, and $C$ lie on line $l$, what is the value of $x$?

• A. $\frac{49}{5}$
• B. $\frac{51}{5}$
• C. $\frac{49}{4}$
• D. $\frac{51}{4}$

Answer 1

The correct option is A $\frac{49}{5}$

Given line l in graph passing through A,B and C

Let the graph is drawn from origin

Since all are squares the coordinates of $A(0,5)$

On moving by 5 units another square is shown of sides 7 units

Hence coordinates of point $B(5,7)$

Since line l is passing through A and B

Equation of line from $A(0,5)$ and $B(5,7)$

$y-5=\frac{7-5}{5-0}x$

$5y-25=2x$

Here coordinates of $C(12,x)$

Since line l passing through C

$5x-25=2\times 12$

$5x-25=24\Rightarrow x=\frac{49}{5}$