PLEASE HELP! can you help me with these math questions im struggling on :,)?
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Answer:
C
Step-by-step explanation:
Calculate AC using Pythagoras' identity in ΔABC
AC² = 20² - 12² = 400 - 144 = 256, hence
AC = = 16
Now find AD² from ΔACD and ΔABD
ΔACD → AD² = 16² - (20 - x)² = 256 - 400 + 40x - x²
ΔABD → AD² = 12² - x² = 144 - x²
Equate both equations for AD², hence
256 - 400 + 40x - x² = 144 - x²
-144 + 40x - x² = 144 - x² ( add x² to both sides )
- 144 + 40x = 144 ( add 144 to both sides )
40x = 288 ( divide both sides by 40 )
x = 7.2 → C
A square has 4 equal sides, which means when you need to work out the area, you're doing length × width, but the length and width are exactly the same, because it's a square (look at the picture if you don't understand this).
That means you just have to pick any side (let's call this side x), and multiply it by another side of the square. Now, because all of the sides are equal, you're doing x multiplied by x, which is the same as x².
Therefore, if the area is equal to x², and in this question, it's also equal to 49 (as stated in the question), we can equate them to each other:
x² = 49
Now to get the x by itself, we need to do the opposite of squaring, which is square rooting. Therefore, we square root both sides of the equation:
√x² = √49
The √ and the ² cancel out, so you're just left with x:
x = √49
The square root of 49 is just 7, so we can replace √49 with 7, and we get:
x = 7
Now remember, earlier, I called x the value of one side. Therefore, by remembering that, you know that the value of one side is equal to 7. And because all the sides are the same as each other, each side is equal to 7 metres.
Therefore, your final answer is 7 metres :)
