Why do people tolerate eccentricity in some people and not in others? Is this fair?

To find the area of that figure, you can find the area how if it was a rectangle and next subtract the area of the triangle in the upper part. The area of a rectangle could be found by the next formula:

Area of a rectangle = base * height

As you can see in the picture, the base is 16 cm and the height is 12 cm, then we replace in the formula:

Area of a rectangle = 16 cm * 12 cm
Area of a rectangle = 192 cm^2

Now, we calculate the area of the triangle to subtract to the area we found and obtain the real area, the formula to obtain the area of a triangle is:

Area of a triangle = (base * height) / 2

The height of the triangle is 8 cm, and the base is 8 cm too, because you subtract to the base of the rectangle (16 cm) the measurements in the upper part (16 - 4 - 4 = 8), Now, we replace in the formula:

Area of a triangle = (8 cm * 8 cm) / 2
Area of a triangle = (64 cm^2) / 2
Area of a triangle = 32 cm^2

We subtract to the found area:

Area of the picture = 192 cm^2 - 32 cm^2
Area of the picture = 160 cm^2

To find the perimeter, you must add all the sides of the picture, but, as you can see, there is a side that doesn't have the measurent, this is the hypotenuse of the triangle used before, but how we know the other sides, we can use Pythagorean theorem:

$a^{2}+b^{2}=c^{2}$

Where:

a = Opposite leg (8 cm)
b = Adjacent leg (8 cm)

So, we replace in the theorem:

$a^{2}+b^{2}=c^{2}$

$(8 cm)^{2}+(8cm)^{2}=c^{2}$ (and we clear c)
$\sqrt{(8 cm)^{2}+(8cm)^{2}} =c$
$\sqrt{64 cm^{2}+64cm^{2}} =c$
$\sqrt{128cm^{2}} =c$
c = 11.3137085 cm
c ≅ 11.31 cm

At last, we add all the sides of the picture begining by the base and going by the left side:

Perimeter of the picture = 16 cm + 12 cm + 4 cm + 11.31 cm + 8 cm + 4 cm + 12 cm
Perimeter of the picture = 67.31 cm approximately.

7 0

3 years ago

The hypotenuse of a 45°-45°-90° triangle measures 128 cm. A right triangle is shown. The length of the hypotenuse is 128 centime

Aleks [24]

Answer:

64√2 or 64 StartRoot 2 EndRoot

Step-by-step explanation:

A 45-45-90 traingle is a special traingle. Let's say one of the leg of the triangle is x. The other one is also x because of the isosocles triangle theorem. Therefore, using the pytagorean theorem, you find that x^2+x^2=c^2. 2(x)^2=c^2. You then square root both sides and get c= x√2.

Therefore, the two legs are x and the hypotenuse is x√2. x√2=128 because the question says that the hypotenuse is 128. Solve for x by dividing both sides by √2. X=128/√2. You rationalize it by multiplying the numberator and denominator of the fraction by √2. √2*√2= 2.

X=(128√2)/2= 64√2 cm.

Since X is the leg, the answer would be 64√2

3 0

3 years ago

Read 2 more answers

Pls help tap picture to see the three problems

valentinak56 [21]

1. Slope intercept form. First find two points to get slope: (0,-3) and (-3,-4). Slope is
(-4 - -3)/(-3 - 0)= 1/3
Use one of the points of (x,y) to solve for b
Y=1/3x + b
-3 = 1/3(0) + b
-3 = b so your slope intercept equation is
Y = 1/3x - 3

2. Rate of Change is slope. Your points are (0,10) and (24,6) so slope is (6-10)/(24-0)
= - 1/6 which means that for each 1 unit increase in x, y decreases by 1/6.

3. Standard form is ax + by =c
Notice it is the same line as in the first graph so it's the same equation
y = 1/3x - 3
First, you cannot have fractions, so you have to multiply the equation by 3 to get rid of the 1/3.
3y= x - 9. Now move the x over:
-x + 3y = - 9. Now get rid of the negative value on x by multiplying the entire equation by -1:
x - 3y = 9

8 0

3 years ago