Math Snap

STEP 1

Assumptions1. The building has a perimeter in the shape of an isosceles triangle.
. The shortest side of the triangle is40 feet shorter than the two longer sides.
3. The perimeter of the triangle is182 feet.

STEP 2

Let's denote the length of the two longer sides as x (since they are equal in an isosceles triangle). Then, the shortest side is x -40.

STEP 3

The perimeter of a triangle is the sum of the lengths of all its sides. So, we can write an equation that represents the perimeter of the triangle.
$$Perimeter = Side1 + Side2 + Side3$$

STEP 4

Now, plug in the values for Side1, Side2, and Side3 to form the equation.
$$182 = x + x + (x -40)$$

STEP 5

implify the equation by combining like terms.
$$182 =3x -40$$

STEP 6

Next, isolate the variable x on one side of the equation. We can do this by adding40 to both sides of the equation.
$$182 +40 =3x -40 +40$$

STEP 7

implify the equation.
$$222 =3x$$

STEP 8

Finally, solve for x by dividing both sides of the equation by3.
$$x =222 /3$$

STEP 9

Calculate the value of x.
$$x =222 /3 =74$$

STEP 10

Now that we have the value of x, we can find the lengths of the three sides of the triangle. The two longer sides are each x feet long, and the shortest side is x -40 feet long.

STEP 11

Plug in the value of x to find the lengths of the sides.
Longer sides $$x =74\, feet$$Shortest side $$x -40 =74 -40$$

Calculate the length of the shortest side.
Shortest side $$x -40 =74 -40 =34\, feet$$The lengths of the three sides of the triangle are74 feet,74 feet, and34 feet.