Question

I got this question wrong, so if someone can please help me with this, I would really appreciate it! Please and thank you!

Answer 1

Explanation:

Area of one of the square=81in^2

Area of square=length×length

A=l^2

Which implies that

81=l^2

√81=√l^2

9=l

Therefore one of the length of the small square is 9

Perimeter of a square=4l

P=4l

Perimeter of the other square=48in

Which implies that

48=4l

48/4=4l/4

12=l

Therefore the length of the other square=12

The two lengths of the right angle triangle are 9 and 12 respectively

To find the length of the largest square we have to find other side of the triangle

Using the formula

a^2+b^2=c^2

a=9 b=12

9^2+12^2=c^2

81+144=c^2

225=c^2

√225=√c^2

15=c

Therefore the length of the other side of the triangle is 15

But the length of the side of the triangle=the side length of the largest square

Therefore the side length of the largest square=15

X=15

Answer 2

15 in.

Explanation:

The area of the left-most square is 81 in.^2. Area = L*W (Length times width), and since we know squares are always equal on each side, we can do 9*9=81. That means the left side of the triangle is 9.

Then, we move to the bottom-most square. The perimeter is 48 in. As said before, we know all sides of a square must be equal. We will divide 48 by 4, as that's how many sides a square has (mind-blowing!), and we get 12. That means, using the Pythagorean Theorem, (9^2) + (12^12) = C^2. We can simplify this to 81 + 144 = C^2, or 225 = C^2 if you add those two numbers together. We can take the square root of both sides to get C = 15!