Respuesta :
Answer:
1. 100 units squared, each side is 10 units
2. a. 16 in squared b. 0.64 cm squared c. 0.0256 units squared. d. [tex]t^{2}[/tex]
3. a. 11cm b. 5/6 in c. 0.4 units d. x units
Step-by-step explanation:
okay this is long. . so for problem 1, you want to use the pythagorean theorem for 1 triangle you see, since all of them have the same side lengths. that would mean you use [tex]a^{2} +b^{2} =c^{2}[/tex] to find the missing side.
so, you know two sides are 8 and 6, so fill in the a and b: [tex]8^{2} + 6^{2} = c^{2}[/tex].
then simplify it. [tex]64 + 36 = c^{2}[/tex] then [tex]100 = c^{2}[/tex]. now you take the square root of both sides because you need c. [tex]\sqrt{100} = \sqrt{c^{2} }[/tex] which means [tex]c = 10[/tex]. then, because the problem asks for the area of the square, you would do 10 times 10, which would give you the area as 100[tex]un^{2}[/tex] (or 100 units squared). For the side lengths, you would say each side length is 10, but you would have to individually name each segment, I'm assuming.
for problem 2:
a: you would do 4 times 4 because the area is length times width. so, the area is 16 in squared.
b: you want to do 0.8 times 0.8 because that is the formula for area. this means the area is 0.64 cm squared.
c: you would do 0.16 times 0.16, which would give you 0.0256 units squared.
d: you would do t times t, which would give you [tex]t^{2}[/tex] because you do not know the value of t.
problem 3:
a: basically, because the area of a square is its side squared, the opposite of a squared is taking the square root. this means that you would take the square root of 121. [tex]\sqrt{121}[/tex], which equals 11, so the answer would be 11 cm.
b: you do the same thing as in a. [tex]\sqrt{(25/36)}[/tex]. with fractions in a square root, you would actually write it like so: [tex]\frac{\sqrt{25} }{\sqrt{36} }[/tex] . then you would solve the roots individually, which would look like this in the end: 5/6, so the answer is 5/6 in.
c: you would take the square root of 0.16. [tex]\sqrt{0.16}[/tex], which is 0.4, so the answer is 0.4 units.
d: you would take the square root of [tex]x^{2}[/tex], which would look like [tex]\sqrt{x^{2} }[/tex]. to do square roots with variables, you would write it out.
