Question

The congruent sides of an isosceles triangle are each one unit longer than the length of the shortest side of the triangle. The perimeter of the triangle is the same as the perimeter of a square whose side length is 2 units shorter than the length of the shortest side of the triangle. What is the length of the shortest side of the triangle?

Answer 1

Answer: congruent sides have equal legnth

the shorter side is the last side

if the congruent sides are x and the shorter one is y, and x is 1 longer than y then

x=1+y

perimiter=x+x+y

x=1+y

perimiter=1+y+1+y+y=3y+2

square is 4s

each side (s) is 2 less than y

s=y-2

square is 4(y-2)=4y-8

4y-8=3y+2

minus 3y both sides

y-8=2

add 8 both sides

y=10

the legnth is 10 units