Question

triangle ABC on the coordinate plane has vertices at A (4,0),B(24,0) and C (24,21). what is the perimeter of triangle ABC? Include a sketch in your answer.

Answer 1

Perimeter = 70

Sketch:

Step-by-step explanation

Step 1: Given

A (4,0),B(24,0) and C (24,21)

Step 2: find the length of AB

`\begin{gathered} AB\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ AB\text{ = }\sqrt[]{(24-4)^2+(0-0)^2} \\ AB\text{ = }\sqrt[]{20^2} \\ AB\text{ = }\sqrt[]{400}\text{ = 20} \end{gathered}`

Step 3: find the length of AC

`\begin{gathered} AC\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ AC\text{ = }\sqrt[]{(24-4)^2+(21-0)^2} \\ AC\text{ = }\sqrt[]{20^2+21^2} \\ AC\text{ = }\sqrt[]{400+441} \\ AC\text{ = }\sqrt[]{841}\text{ = 29} \end{gathered}`

Step 4: find the length of BC

`\begin{gathered} BC\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ BC\text{ = }\sqrt[]{(24-24)^2+(21-0)^2} \\ BC\text{ = }\sqrt[]{21^2} \\ BC\text{ = }\sqrt[]{441}\text{ = 2}1 \end{gathered}`

Step 5: find the perimeter of triangle ABC

`\begin{gathered} \text{Perimeter = AB + AC + BC} \\ \text{Perimeter = 20+29+21 = 70} \end{gathered}`

Hence, the perimeter of triangle ABC is 70.