University:
University of Cambridge
Course:
0580 IGCSE | Mathematics
Academic year:

2023
Views:

245

Pages:

3
Author:

Shahbaz A.

Q 51 Algebra Word Problems Packet No 1 shahbaz ahmed August 2024 Q 51.The perimeter of a triangle is 73 inches. If the second side is 5 inches longer than twice the first side, and the third side is 4 inches less than three times the first side, how long is each side? Solution Let first side=x inches Twice the first side=2x inches Five inches longer than twice the first side=2x+5 inches =⇒Second side= 2x+5 inches Three times the first side=3x inches Four inches less than three times the first side=3x-4 inches The third side =3x-4 inches 1 Perimeter=x+2x+5+3x-4=6x+1 inches Perimeter=73 inches According to the condition 6x + 1 = 73 6x + 1 − 1 = 73 − 1 6x = 72 x= 72 6 = 12 inches First side=12 inches Putting in Second side= 2x+5 inches =⇒ Second side= 2 × 12+5=29 inches Similarly putting x=12 in The third side =3x-4 inches =⇒ The third side =3×12-4=32 inches Checking First side=12 inches Twice the first side= 2×12=24 inches Five inches longer than twice the first side=24+5=29 inches =⇒Second side= 29 inches 2 Three times the first side=3 × 12=36 inches Four inches less than three times the first side=36-4=32 inches The third side =32 inches Also 12 + 29 + 32 = 73 Hence all conditions are satisfied 3