Question

Find the length of LN in the kite below

Answer 1

we can use the pythagorean theorem to find the length of PN in triangle OPN

a²+b²=c²

where a and b are legs and c is the hypotenuse

we are given one leg (OP=8) and the hypotenuse (ON=18) so now we can plug in these numbers to find PN

8²+b²=18²

64+b²=324

b²=260

b=√260

b=√4 * √65

b=2√65

now that we have the value of PN, we can get the value of LN by doubling 2√65

2(2√65) = 4√65

so your answer should be:

LN = 4√65

hope this helped

Answer 2

18^2 - 8^2 = 324 - 64 = 260

PN = √260

LN = 2 PN = 2√260

LN = 32.25