In triangle KAR, MT is drawn in and MT is parallel to AR. KM=6, MA=3, and KT=9. Find the length of KR

Question

How do I solve this problem? A picture of a triangle is also given labeled as in the question description A line MT is in the middle of the triangle and KM is the side while MA is the bottom, and KT is the hypotenuse side. 

Answer 1

triangles KAR and KMT are similar triangles

corresponding sides of similar triangles are proportional, that is, they form equal ratios

KM and KA are corresponding

KT and KR are corresponding

set up a proportion

KM/KT=KA/KR or KM/KA=KT/KR, either way is correct

6/9=9/KR

cross multiply

6*KR=9*9

6*KR=81

KR=81/6=13.5