Question

The sides of a triangle are a + 3 ¼, 2a, and 7 ½ - a. If a = 4 1/8, what is the length of each of the three sides? Also, find the perimeter of the triangle showing steps for your work.

Answer 1

Perimeter = 19 units

Explanation:

Given a = 4 1/8

`Side1 = a + 3(1)/(4)\\Side2 = 2a\\Side3 = 7(1)/(2)-a`

The next step is substituting the a value in the expressions:

`Side1 =  4(1)/(8)+ 3(1)/(4)\\Side2 = 2*(4(1)/(8))\\Side3 = 7(1)/(2)-4(1)/(8)`

Then, fractions with different denominators must be converted to the same denominator. Also, the multiplication of a whole number by a mixed number can be done by using distributive law:

`Side1 =  4(1)/(8)+ 3(2)/(8)\\Side2 = 8(2)/(8)\\Side3 = 7(4)/(8)-4(1)/(8)`

`Side1 =  7(3)/(8)\\Side2 = 8(1)/(4)\\Side3 = 3(3)/(8)`

Now, the perimeter is the sum of all the sides. Therefore, the perimeter is:

`Perimeter =  7(3)/(8) + 8(1)/(4) + 3(3)/(8)`

Which is 19 units.

Answer 2

Answer: Side one is 7 3/8

Side two is 8 2/8

Side three is 3 3/8

Perimeter is 19

Explanation:

The first side is a+3 1/4

the second side is 2a

The third side is 7 1/2-a

Plug 4 1/8 in for a

First side 4 1/8+3 1/4

Find the common denomnator which is 8

4 1/8+3 2/8

7 3/8

First side is 7 3/8

Second side 2(4 1/8)=4 1/8 +4 1/8= 8 2/8

Third side is 7 1/2-4 1/8

Find the common denominator which is 8

7 4/8-4 1/8= 3 3/8

Third side is 3 3/8

The perimeter is adding all the three sides together

7 3/8+8 2/8+ 3 3/8=18 8/8

Reduce 18 8/8=18 +1=19