The length of the rectangle with dimensions 8 cm to 3 cm coincides with the large side of the triangle. If the perimeter of the rectangle and triangle are the same

Question

The length of the rectangle with dimensions 8 cm to 3 cm coincides with the large side of the triangle. If the perimeter of the rectangle and triangle are the same, then how many integral triangles with different dimensions could be drawn?

Answer 1

Perimeter of the rectangle = 2(8+3) = 22 cm

base of the triangle = 8. other 2 sides sum to 22-8 = 14

the difference of the other 2 sides must be greater than 8

x+y = 14

x-y > 8 the difference in 2 sides must be greater than the 3rd side

add the equation & inequality to get

2x > 22 divide by 2

x > 11, x= 12 or 13

y <3 y = 2 or 1

either (x,y) = (12,2) or (13,1)

the other two sides of the triangle are either 12 and 2 or 13 and 1