Question

If LO = 15x+19 and QN = 10x+2 find PN

Answer 1

Answer:

$PN=64\ units$

Step-by-step explanation:

The complete question is

Given the quadrilateral is a rectangle, if LO = 15x+19 and QN = 10x+2 find PN

see the attached figure to better understand the problem

we know that

The diagonals of a rectangle are congruent and bisect each other

so

$QN=\frac{1}{2}LO$

substitute the given values

$10x+2=\frac{1}{2}(15x+19)$

solve for x

$20x+4=15x+19\\20x-15x=19-4\\5x=15\\x=3$

Find the length of PN

Remember that

$PN=LO$ ----> diagonals of rectangle are congruent

$LO=15x+19$

substitute the value of x

$LO=15(3)+19=64\ units$

therefore

$PN=64\ units$