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
Verdich [7]
3 years ago
14

A right triangle has a perimeter of 24 cm and a hypotenuse of 10 cm. Find the length of the other two sides.

Mathematics
2 answers:
jekas [21]3 years ago
7 0

Answer:

One of the sides is 6 cm and the other is 8 cm

Step-by-step explanation:

Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:

a + b + hypotenuse = 24

a + b + 10 = 24

a + b = 14

b = 14 - a

So now we can right the Pythagorean theorem as follows:

a^2 + b^2 = hypotenuse^2\\a^2 + (14-a)^2=10^2\\a^2+ 14^2-28\,a+a^2=100\\2\,a^2-28\,a +96=0\\2\,(a^2-14\,a+48)=0\\2\,(a^2-6\,a-8\,a+48)=0\\2(a\,(a-6)-8\,(a-6))=0\\2\,(a-6)\,(a-8)=0

and from this expression in factor form to be zero a must be 6 or a must be 8.

Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)

or a = 8 (and therefore b = 14 - 8 = 6)

Norma-Jean [14]3 years ago
7 0

Perimeter of triangle = Sum of all sides.

One side of triangle = 10 cm

Measure of other two sides will be → 24-10

Other two sides sum will be = 14 cm

Let's assume one side as x and other as 14-x

Now hypotenuse is of 10 cm

According to Pythagorean theoram

Hypotenuse² = Perpendicular ² + base²

→ 10² = (x)² + (14-x)²

→ 100 = x² + (14-x)²

(a-b)² = a²+b² -2ab

→ 100 = x² + 196 + x² -28 x

→ 100 = 2x² + 196 - 28x

Taking 2 commen both sides

→ 50 = x² -14x + 98

→ 0 = x² -14x +98-50

→ x² -14 x +48 = 0

Factorising :-

→ x² - 6x - 8x + 48 = 0

→ x( x -6) -8(x -6) = 0

→ (x-6)(x-8) = 0

→ x = 6 or x = 8

So x is 6 or 8

Other two sides of triangle are 6 cm and 8 cm

You might be interested in
A club has money for a trip. The expenses for the trip are shown below:
KonstantinChe [14]

Answer:

3/100

Step-by-step explanation:

convert these measurements into one unit, I am going to do decimals but you can sue fractions or percentages as well.

1/4 is 0.25

2/5 is 0.4

0.12 is 0.12

20% is 0.2

if you add all these up, it equals 0.97

1- 0.97= 0.03

you therefore have 0.03 of the money left over

this as a fraction is 3/100

7 0
3 years ago
Helpppp pleaseee i need a quick answer
aleksandr82 [10.1K]

Answer:

32 i think

Step-by-step explanation:

its 16 cm, so 2 full rotations would be 16 times 2

which is 32

4 0
2 years ago
Read 2 more answers
1. is he equation true , false, or open
RideAnS [48]

Question 1:

For this case we have the following equation:

 5x ^ 2 = 6x + 11

We observe that the equation is a polynomial of the second degree.

Therefore, the equation has two possible solutions.

The variable of the equation for this case is x.

In this case, we have an open equation because we have a variable.

Rewriting the equation we have:

5x ^ 2 - 6x - 11 = 0

Answer:

open, there is a variable.


Question 2:

For this case we have the following equation:

 2-8x = -6

From here, we must clear the value of x.

For this, we follow the following steps:

1) Pass the value of 8x adding:

2 = -6 + 8x

2) Pass the value of 6 adding:

2 + 6 = 8x

3) Add the values ​​on the same side of equality:

 8x = 8

4) Pass the 8 to divide:

x = \frac{8}{8} = 1

Answer:

The value of x is given by:

x = 1


Question 3:

For this case we have the following equation:

 y = x-4

The ordered pair solution is the one that satisfies both sides of the equation.

For the point (6, 2) we have:

x = 6  y = 2

Substituting values ​​we have:

2 = 6-4  2 = 2

We observe that both sides of the equation are equal.

Therefore, the ordered pair solution is (6, 2)

Answer:

An ordered pair that is a solution of the equation y = x-4 is:

(6, 2)

3 0
3 years ago
Read 2 more answers
Find the pressure exerted by a force of 240 N on an area of 30 cm2. Find the answer in SI unit​
NeTakaya

Answer:

<u>Pressure</u><u> </u><u>is</u><u> </u><u>8</u><u>0</u><u>,</u><u>0</u><u>0</u><u>0</u><u> </u><u>pascals</u><u>.</u>

Step-by-step explanation:

Area:

= { \bf{ 30 \times  {10}^{ - 4}   \:  {m}^{2} }}

Pressure:

{ \bf{pressure =  \frac{force}{area} }} \\  \\  { \tt{ =  \frac{240}{30 \times  {10}^{ - 4} } }} \\  = { \tt{80000 \: pascals}}

4 0
3 years ago
Please answer!!!! will make brainliest!!!
hammer [34]

Answer:

B

Step-by-step explanation:

1.

  • 3(x+3) - 2 < 4
  • 3x + 9 -2 < 4
  • 3x < 4-7
  • 3x < - 3
  • x < -1
  • x = (-oo, -1)

2.

  • 1 - x ≤ -1
  • - x ≤ -1 - 1
  • -x ≤ -2
  • x ≥ 2
  • x = [2, +oo)

Correct choice is B.

7 0
3 years ago
Other questions:
  • How far is the Moon from the Sun x 500
    9·1 answer
  • Each letter from the word MATHEMATICS is written on a separate slip of paper. The 11th slips of paper are placed in a hat and tw
    15·1 answer
  • What was the names of Jupiter’s big pet dog?
    7·1 answer
  • A supervised learning model has been built to predict whether someone is infected with a new strain of a virus. The probability
    5·1 answer
  • What are the domain and range of the algebraic function you found by graphing the equation y = 36 – 3x? Please hurry I'm being t
    7·1 answer
  • BO is included between
    11·1 answer
  • (35 + 5)[16 + (12 divide 4)]
    10·1 answer
  • I need anyone’s help please. I will give the best answer brainliest.
    11·1 answer
  • Help me pls help me
    11·2 answers
  • The number of students who signed a petition for more​ after-school sports is​ 195, or​ 30% of the students at school.​ Terry's
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!