English Translation
My grandmother attributes her good health to active living.
There are four problems.
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生き方のせいた is an obvious typo. It should be 生き方のせいだ. せいた is spelled as 急いた, meaning “too rush”.
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生き方のせいだ sounds very rude. せいだ suggests that “I” (the speaker) wants my grandmother to die as soon as possible, but she leads a healthy life due to her active lifestyle. There is no nuance of “thanks to” in せいだ. The speaker wants to blame.
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積極的な生き方 is understandable, but it is closer to “proactive life” rather than “active life”. I don’t say it’s wrong but I don’t say that in this context.
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The particle は for the subject is grammatically incorrect. The original Japanese sentence means “My grandmother thinks that someone (not mentioned) is health due to the person’s proactive life. However, I don’t think so.” The particle は functions only as a subject, not an object in this sentence structure. And は is used when comparing the different situations/facts implicitly, and highlighting the gap.
My alternative translation is;
生き生きとした生活環境が、私の祖母の健康の秘訣だ。（いきいきとしたせいかつかんきょうが、わたしのそぼのけんこうのけんこうのひけつだ）
The word-for-word translation in English is “An active life environment is the secret of my grandmother’s health”. 秘訣 is a “secret for success”, so the speaker is happy with my grandmother’s healthy active lifestyle. And 健康の秘訣 is a frequent set phrase.