Using equations to solve problems?

Question

1. the perimeter of a triangle is 74cm. What is the length of each side?

2. the width of a rectangle is one-third the length. The perimeter is 48cm. What is width and length?

3. the perimeter of a regular hexagon is 96cm. What is lengthof each side?

Please tell me the steps, thanks

Answer 1

1) Do you mean equilateral or scalene? You can only answer this if it is a regular, equilateral (all sides the same).

Let S be the length of one side. Then the perimeter is given by the formula
Perimeter = 3S = 74 cm.
3S = 74

Divide both sides by 3:
S = 74/3
S = 24 2/3 cm

Each side of the equilaterlal triangle is 24 2/3 cm.

2) The perimeter of a rectangle is 2(W + L) = 48 cm
You are also told that the width is 1/3 the length. In other words:
3W = L
Perimeter = 2(W + 3W)
Perimeter = 2(4W)
48 = 8W
W = 6 cm
L = 3W = 3(6) = 18 cm.

So the width is 6 cm, the length is 18 cm.

3) A regular hexagon has six sides that are all the same.
The formula for the perimeter is 6S = 96 cm.
6S = 96

Divide both sides by 6:
S = 96 / 6
S = 12 cm

So each side of the regular hexagon is 12 cm.

Answer 2

Answer 1:
What kind of triangle? Isosceles, equilateral, scalene or right-angled?

Answer 2:
Let the length be 'x'
The width is 'x/3'
P = 48cm
2(x + x/3) = 48
x + x/3 = 48/2
x + x/3 = 24
3x/3 + x/3 = 24
(3x + x)/3 = 24
4x/3 = 24
4x = 24*3
4x = 72
x = 72/4
x = 18
The length is 18cm
The width is 18/3 = 6cm

Answer 3:
A regular hexagon has all its sides equal.
Let each side be 'x'
P = 96cm
6x = 96
x = 96/6
x = 16cm
Each side is 16 cm long

Answer 3

1) what type of triangle ?

2) 2(length) + 2(length/3) = 48
8/3 (length) = 48
length = 48 (3/8) = 18cm, width = 6cm

3) hexagon has 6 sides, so 96/6 = 16cm

Answer 4

1. 74=3x (the three comes from the number of sides)
2. 48= 2(1/3)L + 2L
3. 96= 6x