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

Answer: Side one is 7 3/8

Side two is 8 2/8

Side three is 3 3/8

Perimeter is 19

Step-by-step 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

Answer 2

Answer:

Perimeter = 19 units

Step-by-step explanation:

Given a = 4 1/8

$Side1 = a + 3\frac{1}{4}\\Side2 = 2a\\Side3 = 7\frac{1}{2}-a$

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

$Side1 = 4\frac{1}{8}+ 3\frac{1}{4}\\Side2 = 2*(4\frac{1}{8})\\Side3 = 7\frac{1}{2}-4\frac{1}{8}$

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:

$Side1 = 4\frac{1}{8}+ 3\frac{2}{8}\\Side2 = 8\frac{2}{8}\\Side3 = 7\frac{4}{8}-4\frac{1}{8}$

$Side1 = 7\frac{3}{8}\\Side2 = 8\frac{1}{4}\\Side3 = 3\frac{3}{8}$

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

$Perimeter = 7\frac{3}{8} + 8\frac{1}{4} + 3\frac{3}{8}$

Which is 19 units.