Mathematics, 30.09.2019 23:40 Jessietorres2123

Determine whether a triangle can be formed with the given side lengths. if so, use heron's formula to find the area of the triangle. .

given side lengths:
a = 240
b = 133
c = 174

Answers: 2

Show answers

Answers

The triangle inequality theorem states that for a triangle to be formed, none of its side should be greater than the sum of the other two sides. The given satisfy this condition. Therefore, a triangle may be formed.
The area of the triangle is obtained by the Heron's formula,
A = sqrt ((s)(s - a)(s - b)(s - c)) ; s = (a + b + c) / 2
Plugging in the values,
s + (240 + 133 + 174) / 2 = 273.5
A = sqrt ((273.5)(273.5 - 240)(273.5 - 133)(273.5 - 174))j
A = 11317.51 unit²

Answer from: tbiles99

The area of triangle formed by given side lengths is 11317.50.

Step-by-step explanation:

A triangle can be formed If the sum of the other 2 sides (except largest side) is longer than the largest side that is a+b>c

Here, given side lengths:

a = 240

b = 133

c = 174

Here, largest side is a = 240

so taking sum of other two sides,

b+c = 174+133 = 307 > 240

Hence, triangle can be formed with a, b and c as given lengths.

Calculating area using Heron's formula,

first find the semi perimeter by using given sides,

$\text{s}=\frac{\text{a+b+c}}{2}$

$\text{s}=\frac{\text{240+133+174}}{2}=273.5$

$\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}}$

Substitute values of s, a, b and c in above,

$\text{Area}=\sqrt{273.5(273.5-240)(273.5-133)(273.5-174)}}$

$\text{Area}=\sqrt{273.5 \times 33.5 \times 140.5 \times 99.5}}$

$\text{Area}=\sqrt{128085964.44}$

$\text{Area}=11317.50$ (approx)

Thus, the area of triangle formed by given side lengths is 11317.50.

Answer from: Quest

i'm not sure i quite understand, could you provide more information?

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Another question on Mathematics

Mathematics, 21.06.2019 17:00

An airplane consumes fuel at a constant rate while flying through clear skies, and it consumes fuel at a rate of 64 gallons per minute while flying through rain clouds. let c represent the number of minutes the plane can fly through clear skies and r represent the number of minutes the plane can fly through rain clouds without consuming all of its fuel. 56c+64r < 900056c+64r< 9000 according to the inequality, at what rate does the airplane consume fuel while flying through clear skies, and how much fuel does it have before takeoff? the airplane consumes fuel at a rate of gallons per minute while flying through clear skies, and it has gallons of fuel before takeoff. does the airplane have enough fuel to fly for 60 minutes through clear skies and 90 minutes through rain clouds?

Answers: 3

Answer

Mathematics, 21.06.2019 19:30

Two variables, x and y, vary inversely, and x=12 when y=4. what is the value of y when x=3?

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

Choose the equation that represents the graph below: (1 point) graph of a line passing through points negative 3 comma 0 and 0 comma 3 y = x − 3 y = −x + 3 y = −x − 3 y = x + 3 will award !

Answers: 3

Answer

Mathematics, 21.06.2019 21:30

If f(x)=x+7 and g(x)=1/x what is (fog)(x)

Answers: 1

Answer

You know the right answer?

Determine whether a triangle can be formed with the given side lengths. if so, use heron's formula t...

Questions

Mathematics, 30.03.2021 01:20

Solve the equation in the interval from 510° to 1050°. Sin^-1(0)...