Answer:
√408
Step-by-step explanation:
First of all, let's name the top triangle n and the bottom one m, you can name them as you'd like.
okay, so, based on the Pythagorean theorem, a^2 + b^2 = c^2
now, we know that the area that is 12 units long, is equivalent to the hypotenuse of m, (it's very important that the bottom right angle is 90 degrees) and therefore, (5^2 = 25) 5^2 + ___ = 12^2 now let's solve that:
25 + _____ = 144 now just fill in the blank. With a simple subtraction, we get 119 (144 - 25 = 119), now remember, this is c^2 of m
and, 12+5=17 so, a of the n triangle is 17.
so let's put everything together: 17^2 + 119 = x^2
now, we're gonna calculate it: 17^2 = 289 and we're gonna add that to 119, so we get 408: 289 + 119 = x^2
But, this is x^2, and we want to find the value of x, so we have to find the square root of 408. Since we get a number with a lot of decimals in front of it, we're just gonna leave it as is, therefore the answer is √408
Hope it helped!
