Calculate the value of x in each case.

√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!

is only a line? i think so

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it