Given ^MNO = ^PQR,MN = 6 +2y, MO = 2x + 1,PO = 3y + 4, and PR = 10 - X.Find the lengths of PQ and PR.
Accepted Solution
A:
Answer:Part 1) [tex]PQ=10\ units[/tex]Part 2) [tex]PR=7\ units[/tex]Step-by-step explanation:The correct question isThe triangles MNO and PQR are congruent. (MNO≅PQR)Find the lengths of PQ and PR.we know thatIf two figures are congruent, then its corresponding sides are congruentIn this problemMN and PQ are corresponding sidesMO and PR are corresponding sidesNO and QR are corresponding sidesthereforeMN≅PQ MO≅PR NO≅QR step 1Find the value of ywe have[tex]MN = 6 +2y\\ PQ = 3y + 4[/tex]equate the equations[tex]3y + 4=6 +2y[/tex]solve for y[tex]3y-2y=6-4[/tex][tex]y=2[/tex]step 2Find the length of PQ[tex]PQ = 3y + 4[/tex]substitute the value of y[tex]PQ = 3(2) + 4=10\ units[/tex]step 3Find the value of xwe have[tex]MO = 2x + 1\\PR = 10 - x[/tex]equate the equations[tex]2x+1=10-x[/tex]solve for x[tex]2x+x=10-1[/tex][tex]3x=9[/tex][tex]x=3[/tex]step 4Find the length of PR[tex]PR = 10 - x[/tex]substitute the value of x[tex]PR = 10-3=7\ units[/tex]