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
If triangle ABC is congruent to triangle DEF, which statement is not true?
Blizzard [7]
When you name two congruent triangles with the letters of the vertices, you have to keep the order of the corresponding vertices. That means, that when you say triangle ABC is congruent to DEF, the corresponding congruent angles are A = D, B = E, and C = F. regarding the sides, segment AB = segment DE, segment BC = segment EF, and segment CA = segment FD. Then, the answer is that, of the four options,<span> the one that is not true is the option b, because as we already said the corresponding equal angle C is F, not E.</span>
5 0
3 years ago
Whats 9 + 10 fr fr ong fr on fr fr
Fed [463]

Answer:

19.

21 sometimes though.

5 0
2 years ago
Read 2 more answers
What is the value of the 6 in the number 734,906,257 need fasttt
EastWind [94]

Answer:

6 thousands

Step-by-step explanation:

hope it helps

7 0
2 years ago
Read 2 more answers
Which number produces a rational number when added to 0.42
kenny6666 [7]
Any Whole or Rational Number, 1 can be used as an Example if you want it Simple

4 0
3 years ago
An arena is hosting a concert. At the most, the arena can hold 8,500 people. If tickets have already been sold to 6,900 people,
ElenaW [278]

Answer:

Subtract 6,900 from 8,500 to get the highest number of tickets that can still be sold which is 1,600.

8 0
2 years ago
Other questions:
  • All real numbers no more than five units from -14
    12·1 answer
  • If a car is worth ​$4900when it is 4years​ old, how old will it be when it is worth ​$2800​
    5·1 answer
  • Which is the other endpoint of a line segment with one endpoint at (-2, 5) and midpoint at (3, 1)?
    14·2 answers
  • What are the answers to 1 5 3 and 6 really aprreciate it!
    12·1 answer
  • Please help with the question!!!!!
    10·2 answers
  • Factor 9x^3y-25xy^3 completely.
    6·2 answers
  • I need the answers to the 2 blanks
    6·1 answer
  • Sandy borrowed a book from Liabrary and read notice about fines. Each day fine doubles.if snook is 1day overdue ,the fine is $0.
    6·1 answer
  • Factor this trinomial completely. -12x^2+45x+12
    8·2 answers
  • Zen design a character for a video game he just three sizes of the character on grid paper then uses the expression 6+ X to the
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!