I am aware that the yuga lengths have the ratio 4:3:2:1 and have seen in various posts that a Kali Yuga is 432,000 years. What religious texts (Puranas, Mahabharat, Ramayan, etc) mention these Yuga lengths? If possible, can one site the words from these religious texts.
I have given below a discussion of the length of the yugas in Linga Purana.
O brahmins, the Krta yuga consists of four thousand years. Four hundred, three hundred, two hundred and hundred years respectively constitute the period of transition both at the beginning and end of a yuga. 
Linga Purana I.4.5-6
 Each Yuga is prefixed and suffixed by a sandhya which specifies the advent and culmination of yuga. The two sandhyas of a yuga are of equal length though their period of duration differs from yuga to yuga. Thus Krta Yuga lasts for four thousand divine years and its sandhyas for eight hundred such years; Treta lasts for three thousand divine years and its sandhyas for six hundred such years; Dvapara lasts for two thousand years and its sandhyas for four hundred; Kali lasts for one thousand and its sandhyas for two hundred such years. The total period for the four yugas is ten thousand divine years and that for their sandhyas is two thousand divine years.
The amsaka, therefore, is one-sixth of the duration of each yuga. The period of duration of Treta, Dvapara and kali is respectively three thousand, two thousand and one thousand years without their amsaka parts.
Linga Purana I.4.7-8
The above two passages give us the duration of the yugas in divine years. Now we have to change the duration into human years.
The people who know arithmetic say that the three hundred and sixty thousand human years constitute the period of a thousand divine years.
Linga Purana I.4.23
The duration of a yuga is calculated according to the divine reckoning. The first yuga is name Krta; thereafter comes Treta and then Dvapara and Kali. O men of holy rites, these are the (names of the four) yugas. Henceforth the number of years of each yuga which have been mentioned earlier in divine reckoning are now being counted according to human reckoning. The Krta consists of one million four hundred and forty thousand human years; Treta of one million eighty thousand years; Dvapara of seven hundred twenty thousand years and Kali of three hundred and sixty thousand human years; Thus the duration of the four yugas without the period of junction and transition totals to three million six hundred thousand human years. If Sandhya period is included, the set of four ages will consist of four million three hundred and twenty thousand years.
Linga Purana I.4.24-30
Its not that direct, we need to calculate it! From the Shri-Surya-Siddhanta, Chapter 1 Verse 17
युगस्य दशमो भागश्चतुस्त्रिद्वेकसंगुण: । क्रमात् कृतयुगादीनां षष्ठांश: सन्ध्ययो: स्वक:॥ १७॥
The tenth part of the age, multiplied successively by 4, 3, 2 and 1 gives length of golden and other ages in order. The sixth part of it belongs to its Dawn and twilight.
1 Maha-Yuga = 12000 Divine Years 1/10-th of 12000 = 1200 divine years
Now the ages starting from satya-yuga (Golden age) are:
Satya-yuga : 4×1200 = 4800 Dwapar-yuga: 3×1200 = 3600 Treta-yuga: 2×1200 = 2400 Kali-yuga: 1×1200 =1200
Note: To convert to human years use
1 Divine year = 360 Human years.
Also out of total years of a yuga, 1/6th of it is a transition time.
satya-yuga: 4800/6 = 800 Divine Years. (400 + 400 Devine years)
In the case you are wondering how the measurement of a mahayuga arrives:
महायुगप्रमाणम्- तद्द्वाशशसहस्ताणि च॒तुर्युगमुदाहतम् । सूर्याब्दसड्ख्यया ब्रित्रिसागरैरयुताहतै: ॥ १५ ॥ सन्ध्यासन्ध्यांशसहितं विज्ञेयं तच्चतुर्युगम् । कृतादीनां व्यवस्थेयं धर्मपादव्यवस्थया ॥ १६ ॥
In terms of the units of divine years, Twelve thousand of these years are denominated to a Quardruple Age (Chaturyuga) I.e. of ten thousand times four hundred and thirty two solar years. This Chaturyuga ( Mahayuga) is mesured by including the transition time (Dwan and twilight). The difference in the four yugas is according to the difference of feets of Dharma.
The Bull stands on all four legs in satya yuga thus its the longest, while he stands only on one thus Kali is smallest.
Vishnu Purana: Book I: Chapter III mentions that one Manwantara is equal to 71 Chaturyuga or 306720000 human years:
a Manwantara, is equal to seventy-one times the number of years contained in the four Yugas, with some additional years: this is the duration of the Manu, the (attendant) divinities, and the rest, which is equal to 852000 divine years, or to 306720000 years of mortals*
1 Chauturyuga = 306720000 / 71 = 4320000 human years
As you have mentioned, the yuga length ratio is: 4:3:2:1 (Satya:Treta:Dwapara:Kali).
So, Kaliyuga duration would be: 1 / (4+3+2+1) * 4320000 = 4,32,000 human years