Question

The perimeter of a triangle with 2 equal sides is 42 cm. If its base were lengthened by 7 cm and each leg were shortened by 5 cm, all 3 sides would be equal. Find the length of the base the original triangle.

Answer 1

base = 6

Answer 2

2x+b = 42
b+7 = x-5

solve for b

Answer 3

You need to solve simultaneous equations.
For the 1st triangle, let the two equal sides be x, and the base be y, then you get
2x+y = 42
for the 2nd triangle, the base is y+7, and the two equal sides are each x-5.
Then you're also told that the 2nd one is equilateral, that is y+7 = x-5
So equation 1: 2x+y=42
Equation 2: x-y=12 ( after rearranging the y+7=x-5 )

Answer 4

let x = leg
y = base

42 = 2x + y
3x = y+7 + 2(x - 5)
3x = y + 7 + 2x - 10
x = y - 3

2x + y = 42
x - y = -3
3x = 39
x = 13
y = 16 cm is the orig base