Question

20. GEOMETRY The measures of two sides of a triangle are given. If p isthe perimeter, and p=10x+5y, find the measure of the third side (3x+4y, 5x-y)

Answer 1

The perimeter of any shape is a measure of the length of the peripheral of that shape.

For a triangle, it is an addition of the length of the 3 sides.

P = a + b + c where a, b, c are the lengths of the individual sides.

p = 10x + 5y = (3x + 4y) + (5x - y) + c

Collecting like terms on the RHS, we have

p = 10x + 5y = 8x + 3y + c

Subtracting 8x + 3y from both sides to give c leaves us with

10x + 5y - (8x + 3y) = c

c = 10x - 8x + 5y - 3y

c = 2x + 2y