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2 years ago

15

Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.

1 answer:

Archy [21]2 years ago

8 0

<u>The correct answer is </u><u>8.5 in.</u>

<h3 /><h3>What is Heron's formula in math?</h3>

Heron's formula, formula credited to Heron of Alexandria for finding the area of a triangle in terms of the lengths of its sides.
In symbols, if a, b, and c are the lengths of the sides: Area = Square root of√s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.

we know that

The formula of area of triangle is equal to

$A = \frac{1}{2} (b) (h)$

We have

b = BC = 6 in

h = AD = x in

substitute

$A = \frac{1}{2} (6) (x)$

$A = 3x^{2} in^{2} ..................(1)$

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.

Let a,b,c be the lengths of the sides of a triangle.

The area is given by:-

$A = \sqrt{p(p-a) (p-b) (p-c)}$ where p is half the perimeter

$p = \frac{a +b+ c}{2}$

a = 9 in , b= 9 in, c = 6 in

$p = \frac{9 + 9 + 6}{2} = 12 in$

Find the area

$A = \sqrt{12( 12 - 9) (12-9) (12 - 6)}$

$A = \sqrt{12 (3)(3)(6)}$

$A = \sqrt{648}$

$A = 25.46 in^{2}$

Substitute the value of the area in the equation 1 and solve for x

$A = 3x in^{2}$

25.46 = 3x

x = 25.46/3

x = 8.5 in

Learn more about Heron's Formula

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7. All of the following are perfect square trinomials EXCEPT one. Which is it?

wolverine [178]

Answer:

All answers EXCEPT answer C. are perfect square trinomials.

Step-by-step explanation:

A perfect square trinomial is polynomial that satisfies the following condition:

$(a+b)^{2} = a^{2}+2\cdot a \cdot b + b^{2}$ , $\forall\,a,b\in\mathbb{R}$

Let prove if each option observe this:

a) $4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}$

1) $4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}$ Given

2) $(2\cdot x)^{2}+ 2\cdot (2\cdot x)\cdot (3\cdot y)+(3\cdot y)^{2}$ Definition of power/Distributive, associative and commutative properties.

3) $a = 2\cdot x$ , $b = 3\cdot y$ Definition of perfect square trinomial/Result.

b) $9\cdot a^{2}-36\cdot a + 36$

1) $9\cdot a^{2}-36\cdot a + 36$ Given.

2) $(3\cdot a)^{2}-2\cdot (3\cdot a)\cdot 6 + 6^{2}$ Definition of power/Distributive, associative and commutative properties.

3) $a = 3\cdot a$ , $b = 6$ Definition of perfect square trinomial/Result.

c) $x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}$

1) $x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}$ Given

2) $x\cdot y\cdot (1-4\cdot x+4\cdot x)$ Distributive property.

3) $x\cdot y \cdot 1$ Existence of the additive inverse/Modulative property.

4) $x\cdot y$ Modulative property/Result.

d) $a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}$

1) $a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}$ Given

2) $(a\cdot b)^{2}+2\cdot (a\cdot b)\cdot (2\cdot a^{2})+(2\cdot a^{2})$ Definition of power/Distributive, associative and commutative properties.

3) $a = a\cdot b$ , $b = 2\cdot a^{2}$ Definition of perfect square trinomial.

All answers EXCEPT answer C. are perfect square trinomials.

8 0

3 years ago

PLEASE HELP!!!!

pogonyaev

Answer:

30.667, in 1 hour = 40 miles

Step-by-step explanation:

Set up a proportion so 1.5 miles / 2.25 minutes.

So 1.5/2.25 = x/46

solve for x 1.5(46)/2.25 = x so x = 30.667

In one hour is 60 minutes so 1.5(60)/2.25 = x

8 0

3 years ago

I neeeeed heeeeeeeeeeelp

xenn [34]

The answer is C for that question

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3 years ago

Read 2 more answers

PLEASE HELP !! ILL GIVE 40 POINTS ; PLUS BRAINLIEST !! DONT SKIP ANSWER.

Natalija [7]

Answer:
GFC and BCF ??

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3 years ago

Simplify the expression √6 (√33=7)

marin [14]

14.07 is the answer to the question above

7 0

3 years ago