# What is the perimeter of a triangle with corners at (7 ,9 ), (8, 2 ), and (9 ,4 )?

Perimeter $P = 5 \sqrt{2} + \sqrt{5} + \sqrt{29} = 14.6923 \text{ }$units

#### Explanation:

compute lengths of sides:

${d}_{1} = \sqrt{{\left(7 - 8\right)}^{2} + {\left(9 - 2\right)}^{2}} = 5 \sqrt{2}$
${d}_{2} = \sqrt{{\left(8 - 9\right)}^{2} + {\left(2 - 4\right)}^{2}} = \sqrt{5}$
${d}_{3} = \sqrt{{\left(7 - 9\right)}^{2} + {\left(9 - 4\right)}^{2}} = \sqrt{29}$

Perimeter $P = \sqrt{50} + \sqrt{5} + \sqrt{29} = 14.6923 \text{ }$units

God bless....I hope the explanation is useful.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://socratic.org/questions/what-is-the-perimeter-of-a-triangle-with-corners-at-7-9-8-2-and-9-4", "fetch_time": 1657111317000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2022-27/segments/1656104672585.89/warc/CC-MAIN-20220706121103-20220706151103-00656.warc.gz", "warc_record_offset": 588215831, "warc_record_length": 6268, "token_count": 251, "char_count": 577, "score": 4.28125, "int_score": 4, "crawl": "CC-MAIN-2022-27", "snapshot_type": "latest", "language": "en", "language_score": 0.5225682854652405, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00060-of-00064.parquet"}