Question

A is between C and T CA=4x-1, AT=2x-1, and CT=5x. Find the value of x and the length of AT. ( Draw a picture)

O is the midpoint of DG. Do=4x+2 and OG= x +14. find c and the length of DG (draw picture)

Answer 1

The value of x is 2 and the length AT is 3

The value of x is 4 and DG is 36

How to determine the values of x and length AT

From the question, we have the following parameters that can be used in our computation:

A is between C and T

Also, we have

CA = 4x - 1

AT = 2x - 1

CT = 5x

This means that

4x - 1 + 2x - 1 = 5x

Evaluate the like terms

6x - 2 = 5x

So, we have

x = 2

For AT, we have

AT = 2x - 1

AT = 2 * 2 - 1

AT = 3

How to determine the values of x and length DG

Here, we have

O is the midpoint

Also, we have

DO = 4x + 2

OG = x + 14

This means that

4x + 2 = x + 14

So, we have

3x = 12

Evaluate

x = 4

For DG, we have

DG = 4x + 2 + x + 14

DG = 4 * 4 + 2 + 4 + 14

DG = 36

Hence, the value of x is 4 and DG is 36