1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Marizza181 [45]
3 years ago
12

The sides of a triangle are x , x +1 , 2 x -1 and its area is x root of 10 .Find the value of x.

Mathematics
1 answer:
VARVARA [1.3K]3 years ago
6 0


Ok, I'm going to start off saying there is probably an easier way of doing this that's right in front of my face, but I can't see it so I'm going to use Heron's formula, which is A=√[s(s-a)(s-b)(s-c)] where A is the area, s is the semiperimeter (half of the perimeter), and a, b, and c are the side lengths.

Substitute the known values into the formula:

x√10=√{[(x+x+1+2x-1)/2][({x+x+1+2x-1}/2)-x][({x+x+1+2x-1}/2)-(x+1)][({x+x+1+2x-1}/2)-(2x-1)]}

Simplify:

<span>x√10=√{[4x/2][(4x/2)-x][(4x/2)-(x+1)][(4x/2)-(2x-1)]}</span>

<span>x√10=√[2x(2x-x)(2x-x-1)(2x-2x+1)]</span>

<span>x√10=√[2x(x)(x-1)(1)]</span>

<span>x√10=√[2x²(x-1)]</span>

<span>x√10=√(2x³-2x²)</span>

<span>10x²=2x³-2x²</span>

<span>2x³-12x²=0</span>

<span>2x²(x-6)=0</span>

<span>2x²=0 or x-6=0</span>

<span>x=0 or x=6</span>

<span>Therefore, x=6 (you can't have a length of 0).</span>

You might be interested in
Please EXPLAIN how to get this answer so I can do it with other problems. A straight answer would be great, but I have to do abo
OLEGan [10]

Answer:

PQ = 3.58, and RQ = 10.4

Step-by-step explanation:

We are given the hypotenuse of the triangle, and an angle. Use sin and cos to solve.  

Hypotenuse = 11,

Opposite side is PQ

Adjacent side is RQ

x = 19

Sin x  = (opposite side)/(hypotenuse)

Cos x = (adjacent side)/(hypotenuse)

For PQ, this is the side opposite to the angle, so use sin,

Sin 19 = x/11

   11(Sin 19) = x

        3.58 = x        (rounded to the nearest hundredth)            

For RQ, this is the side adjacent to the angle, so use cos,

Cos 19 = x/11

   11(Cos 19) = x

        10.4 = x        (rounded to the nearest hundredth)        

6 0
3 years ago
Use signed numbers to solve. A helicopter descended 1200 feet, rose 800 feet, and then descended 450 feet. What was the net gain
DENIUS [597]
B. Lost 850 ft
800-450= 350
1200-350=850

I hope I helped :D

6 0
3 years ago
A plate has a diameter of 4 inches . What is the area of the plate ?
igor_vitrenko [27]

Answer:

12.56 inches^2

Step-by-step explanation:

To solve this we use pi*r^2

Radius is diameter/2

so the equation is pi*2^2

pi*4

12.56 inches^2

6 0
3 years ago
Read 2 more answers
Show how you can determine that the inscribed figure inside a quadrilateral is a parallelogram. Support your argument with diagr
denis23 [38]

Answer:

Look for perpendicular lines or corresponding angles or alternate interior angles.

Step-by-step explanation:

When you want to show that a quadrilateral is a parallelogram you need to show that the oposite sides are parallel. In order to show that two segments are parallel there are various theorems and definitions you can use.

1 -  Remember that two lines perpendicular to the same segment are parallel.

2 - When two lines are cut by a secant and their alternate interior angles are congruent, then the resulting lines are parallel, I will attach a drawing to illustrate what I am saying.

3 - When two lines are cut by a secant and their CORRESPONDING angles are congruent, then the resulting lines are parallel, I will also attach a drawing to illustrate what I am saying.

6 0
3 years ago
What is the quotient of 13 divided by 8
Masteriza [31]
1.625 or/and 13/8 should be your answer
8 0
2 years ago
Other questions:
  • Find the value of x in each of the following
    12·1 answer
  • What's the answer????​
    7·1 answer
  • suppose a parabola has a vertex of (-4 7) and also passes through the point (-3,8). what is the equation of the parabola in vert
    9·2 answers
  • I don’t know why i’m confused on this one
    15·1 answer
  • 6m + 15n- 12p/n for m = -3.5, n=4, and p=3
    9·2 answers
  • If a customer at a particular grocery store uses coupons, there is a 50% probability that the customer will pay with a debit car
    12·1 answer
  • Colin gets £xx wages each week. After he pays his tax of £tt, he then pays his rent of £250. He shares what's left between himse
    10·1 answer
  • Se han gastado 5/9 de la capacidad de un depósito u aun quedan 108L. Cuál es la capacidad del depósito?
    9·1 answer
  • HELPPP plzzzzzz im so lost i hate math -.-
    12·2 answers
  • The area of the entire figure below is 111 square unit.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!