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postnew [5]
3 years ago
10

How do you solve for area and perimeter

Mathematics
1 answer:
OverLord2011 [107]3 years ago
8 0
Find the measure of the third angle

Use your trig functions the get the sides

Then calculate area and perimeter
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Among all right triangles whose hypotenuse has a length of 12 cm, what is the largest possible perimeter?
Veronika [31]

Answer:

Largest perimeter of the triangle =  

P(6\sqrt{2}) = 6\sqrt{2} + \sqrt{144-72} + 12 = 12\sqrt{2} + 12 = 12(\sqrt2 + 1)

Step-by-step explanation:

We are given the following information in the question:

Right triangles whose hypotenuse has a length of 12 cm.

Let x and y be the other two sides of the triangle.

Then, by Pythagoras theorem:

x^2 + y^2 = (12)^2 = 144\\y^2 = 144-x^2\\y = \sqrt{144-x^2}

Perimeter of Triangle = Side 1 + Side 2 + Hypotenuse.

P(x) = x + \sqrt{144-x^2} + 12

where P(x) is a function of the perimeter of the triangle.

First, we differentiate P(x) with respect to x, to get,

\frac{d(P(x))}{dx} = \frac{d(x + \sqrt{144-x^2} + 12)}{dx} = 1-\displaystyle\frac{x}{\sqrt{144-x^2}}

Equating the first derivative to zero, we get,

\frac{dP(x))}{dx} = 0\\\\1-\displaystyle\frac{x}{\sqrt{144-x^2}} = 0

Solving, we get,

1-\displaystyle\frac{x}{\sqrt{144-x^2}} = 0\\\\x = \sqrt{144-x^2}}\\\\x^2 = 144-x^2\\\\x = \sqrt{72} = 6\sqrt{2}

Again differentiation P(x), with respect to x, using the quotient rule of differentiation.

\frac{d^2(P(x))}{dx^2} = \displaystyle\frac{-(144-x^2)^{\frac{3}{2}}-x^2}{(144-x)^{\frac{3}{2}}}

At x = 6\sqrt{2},

\frac{d^2(V(x))}{dx^2} < 0

Then, by double derivative test, the maxima occurs at x = 6\sqrt{2}

Thus, maxima occurs at x = 6\sqrt{2} for P(x).

Thus, largest perimeter of the triangle =  

P(6\sqrt{2}) = 6\sqrt{2} + \sqrt{144-72} + 12 = 12\sqrt{2} + 12 = 12(\sqrt2 + 1)

7 0
3 years ago
Evaluate the expression(-3.8)+0+y for the given values of y.
11111nata11111 [884]

Answer:

y = -3.3 then  -7.1

y = -7.1 then  -10.9

y = -2.6 then -6.4

y = 1 then -2.8

y = 4.2 then 0.4

Step-by-step explanation:

(-3.8)+0+y can be simplified to -3.8 + y. Evaluate each value for y by substituting it into the expression and solving.

y = -3.3 then -3.8 + -3.3 = -7.1

y = -7.1 then -3.8 + -7.1 = -10.9

y = -2.6 then -3.8 + -2.6 = -6.4

y = 1 then -3.8 + 1 = -2.8

y = 4.2 then -3.8 + 4.2 = 0.4

7 0
3 years ago
Helps, also explain how to do it I want to learn how and stop using brainy​
Nutka1998 [239]

Answer:

259

Step-by-step explanation:

USE PEMDAS

Parenthesis

Exponent

Multiplication

Division

Addition

Subtraction

5 0
3 years ago
I have no idea what to do with this someone help
joja [24]
The given distance of 5.20 would be A.

Replace A with 5.20 to solve for T.

T = 5.20^3/2
T = 11.9 years.
4 0
3 years ago
Read 2 more answers
Prove the polynomial identity. (2x−1)2+2(2x−1)=(2x+1)(2x−1) Drag and drop the expressions to correctly complete the proof of the
Alex_Xolod [135]

Answer:

Step-by-step explanation:

Given expression is,

(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)

To prove this identity we will take the left hand side of the equation and will prove equal to the right side.

(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)

4x² - 4x + 1 + 4x - 2 = (2x - 1)(2x + 1)

4x² - 1 = (2x - 1)(2x + 1)

(2x - 1)(2x + 1) = (2x - 1)(2x + 1) [Since a² - b² = (a - b)(a + b)]

6 0
4 years ago
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