SOLUTION: A banner in the shape of an isosceles triangle has a base that is 2 inches shorter than either of the equal sides. If the perimeter of the banner is 43 inches, then what is the len

Question 211581: A banner in the shape of an isosceles triangle has a base that is 2 inches shorter than either of the equal sides. If the perimeter of the banner is 43 inches, then what is the length of the equal sides?
Thx
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Recall that the perimeter of any triangle is

P = length of side1 + length of side2 + length of side3

Now let
x = length of side1
y = length of side2
z = length of side3

So the perimeter is now . Because the triangle is an isosceles, there are two sides that are equal. So let's make which will make the base be 'x'. Since the "triangle has a base that is 2 inches shorter than either of the equal sides", this means or

Start with the given equation.

Plug in (the given perimeter), , and

Combine like terms.

Add to both sides.

Combine like terms.

Divide both sides by to isolate .

Reduce.

Rearrange the equation.

Since , we know that also. So the length of the equal sides is 15 inches. Subtract 2 from this to get 13

==================================================

Answer:

So the triangle has side lengths of 13, 15, and 15 inches

RELATED QUESTIONS
A banner in the shape of an isosceles triangle has a base that is 5 inches shorter than... (answered by Earlsdon)

A banner in the shape of an isosceles triangle has a base that is 5 inches shorter than... (answered by checkley77)

A banner in the shape of an isosceles triangle has a base that is 3 inches shorter than... (answered by scott8148)

a flag in the shape of an isosceles triangle has a base that is 3.5 inches shorter than... (answered by CharlesG2)

A banner is in the shape of a right triangle of area 63 in^2. The height of the banner is (answered by Fombitz,macston,MathTherapy)

And isosceles triangle has a perimeter of 17 inches with its two shorter sides equal in... (answered by poliphob3.14)

A sailboat sail in the shape of an isosceles triangle has a base that is 9 feet longer... (answered by mangopeeler07,stanbon)

An isosceles triangle has a perimeter of 45 in. If the two congruent sides are 5 inches... (answered by cleomenius)

An isosceles triangle has a base which is 3 inches shorter that any of the two sides. If... (answered by josgarithmetic)