Question

If our bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 27 feet more than the length of the shortest side find the dimensions if the perimeter is 167 feet

Answer 1

Answer: 35 feet, 70 feet, and 62 feet.

Explanation:

According to the problem, one side of the triangle is twice the length of the shortest side. So, the second side would be 2x feet.

The third side is given as 27 feet more than the length of the shortest side. Therefore, the third side is x + 27 feet.

To find the dimensions of the triangle, we need to determine the values of x, 2x, and x + 27 that satisfy the given perimeter of 167 feet.

The perimeter of a triangle is found by adding up the lengths of all its sides. In this case, the perimeter is given as 167 feet.

To solve for x, we can set up the following equation:

x + 2x + (x + 27) = 167

Combining like terms:

4x + 27 = 167

Subtracting 27 from both sides:

4x = 140

Dividing both sides by 4:

x = 35

Now that we know the value of x, we can find the dimensions of the triangle:

The shortest side is x feet, so it is 35 feet.

The second side is 2x feet, so it is 2 * 35 = 70 feet.

The third side is x + 27 feet, so it is 35 + 27 = 62 feet.

Therefore, the dimensions of the triangle are 35 feet, 70 feet, and 62 feet.

Answer 2

35ft , 62ft and 70ft

Explanation:

Let the length of the shortest side of the triangular bed be x feet. Then the length of the second side is 2x and the length of the third side is x + 27.

The perimeter of the triangle is equal to the sum of the lengths of the three sides. We are given that the perimeter is 167 feet, so we can set up the following equation:

x + 2x + (x+27) = 167

Simplifying the equation, we get

4x + 27 = 167

Subtracting 27 from both sides, we get:

4x + 27 - 27 = 167 - 27

4x = 140

Dividing both sides by 4, we get:

`\sf (4x )/(4)=(140)/(4)`

x = 35

Now that we know the length of the shortest side, we can find the length of the other two sides:

Second side: 2x = 2 × 35 = 70 feet

Third side: x + 27 = 35 + 27 = 62 feet

Therefore, the dimensions of the triangular bed are 35 feet, 70 feet, and 62 feet.