Question

The congruent sides of an isosceles triangle are each 1 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

10 units

Explanation:

Let the shortest side be x

Now since we are given that The congruent sides of an isosceles triangle are each 1 unit longer than the length of the shortest side of the triangle.

So, the length of the congruent sides (each) = x+1

Thus the perimeter of triangle = sum of all sides

= x+x+1+x+1

=3x+2

Now we are given that 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.

Side of square = x-2

So, perimeter of square = 4*side

=4(x-2)

=4x-8

Now since the perimeter of the triangle and square are equal

So,
`3x+2=4x-8`

`10=x`

Hence the shortest side of the triangle is 10 units.

Answer 2

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