Question

In parallelogram RNCS, BC and AR are perpendicular to diagonal NS, and AB = 10 ft. If NS = 28, then how long are BN and AS?

Answer 1

My first guess is 9 ft. I am thinking triangles RAN and CBS are similar. But need to do some more research.

Answer 2

What do you think??

Answer 3

i do nt kno how 2 do it

Answer 4

Those two triangles have equal sides RN and SC because of definition of parallelogram.

Answer 5

I want to believe RA equal BC because the hypotenuses are equal (RN = CS)

Answer 6

If that is the case then the two triangles are equal and the answer would be 9 ft.

Answer 7

triangle RAS and triangle CBN are congruent by AAA property.

So, BN=AS =x(say) (corresponding sides of congruent triangles)

AB + AS + BN =NS
10 + x + x =28
x=9 ft. =AS =BN

Answer 8

Thanks A_clan, I thought it was 9, but was struggling for proof.