Question

The length of the sides of a quadrilateral are $x,3x+1,2x-3,$ and $x+5$ inches respectively. If the sum of the length of the sides of the quadrilateral is $24$ inches, the longest side is

• A. $12$
• B. $10$
• C. $9$
• D. $7$

Answer 1

The correct option is B $10$

Given sides: $x,3x+1,2x-3,$ and $x+5$ inches

Sum of the length of the sides: $18$ inches

So,
$x+(3x+1)+(2x-3)+(x+5)=23$

$x+3x+2x+x+1-3+5=23$

$7x+3=24$

$7x=24-3$

$7x=21$

$x=\frac{21}{7}$

$x=3$

Therefore, sides are $x=3,3x+1=10,2x+3=9,$ and $x+5=8$ inches respectively.

Thus, the longest side has length $10$ inches.