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
yKpoI14uk [10]
2 years ago
14

The hypotenuse of a right angled triangle is 2√13 cm . If the smaller side is increased by 2 cm and the larger side is increased

by 3 cm , the new hypotenuse will be √117 cm . Find the length of the larger side of the right angled triangle .​
Mathematics
1 answer:
White raven [17]2 years ago
6 0

<em><u>Statement:</u></em>

The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.

<em><u>To find out:</u></em>

The length of the larger side of the right angled triangle.

<em><u>Solution:</u></em>

Let us consider x as the smaller side and y as the larger side.

Then, in the right angled triangle,

x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]

Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).

And if the larger side is increased by 3 cm, then the larger side will be (y + 3).

Then, in the new right angled triangle,

(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]

or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²

or, x² + 4x + 4 + y² + 6y + 9 = (√117)²

or, x² + y² + 4x + 6y + 13 = (√117)²

Now, put the value of x² + y² from equation (I),

or, (2√13)² + 4x + 6y + 13 = (√117)²

or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)

or, 52 + 4x + 6y + 13 = 117

or, 4x + 6y = 117 - 52 - 13

or, 4x + 6y = 52

or, 4x = 52 - 6y

or, x = \frac {(52 - 6y)}{4} ...(II)

Now, put the value of x of equation (II) in (I),

x² + y² = (2√13)²

or, \frac {(2704-624y +36y²)}{16} + y² = 52

or, \frac {(2704-624y +36y² + 16y²)}{16}= 52

or, 52y²-624y + 2704 = 52 × 16

or, 52y² - 624y + 2704 - 832 = 0

or, 52y² - 624y + 1872 = 0

or, 52(y² - 12y + 36) = 0

or, y²-12y +36 = 0 ÷ 52

or, y²-12y +36 = 0

or, (y)² - 2 × 6 × y + (6)² = 0

or, (y - 6)² = 0

or, y - 6=0

or, y = 6

We have taken y as the length of the larger side of the right angled triangle.

So, the length of the larger side is 6 cm.

<em><u>Answer:</u></em>

6 cm

Hope you could understand.

If you have any query, feel free to ask.

You might be interested in
D’Andra has a dentist appointment in 5 weeks. There are 7 days in a week. How many days are in 5 weeks?
Lisa [10]

Answer:

A. 35

Step-by-step explanation:

Each week has 7 days, and we have 5 weeks.

Week 1 has 7 days.

Week 2 has 7 days.

Week 3 has 7 days.

Week 4 has 7 days.

Week 5 has 7 days.

We can add all these together to get the total number of days: 7 + 7 + 7 + 7 + 7 = 7 * 5 = 35.

Thus, the answer is A.

Hope this helps!

8 0
3 years ago
Read 2 more answers
Perimeter = 24 meters<br> (x + 3) m<br> 2.xm
Pani-rosa [81]

Answer:

umm

Step-by-step explanation:

5 0
3 years ago
PLEASE Help ASAaP will give brainlist
pychu [463]
Answer: yes they probably are because they can be any size
3 0
3 years ago
Solve the following triangle in which given sides are<br> a=7 b=7 c=9
blagie [28]
We have an isosceles triangle;
A=opposite angle side a.
B=opposite angle side b.
C=opposite angle side c.

A=B
Method 1:

We can divide the isosceles triangle in two right triangles,
hypotenuse=7
side=9/2=4.5

B=A=arccossine (4.5/7)=49.994799...º≈50º
C/2=90º-50º=40º  ⇒ C=2*40º=80º

Answer:
a=7;  A=50º
b=7;  B=50º
<span>c=9;  C=80º

Method 2:
Law of cosines:
a²=b²+c²-2bcCosA  ⇒CosA=(a²-b²-c²)/(-2bc)
CosA=(49-49-81) / (-126)=0.642857
A=arco cos (81/126)≈50º

B=A=50º

A+B+C=180º
50º+50º+C=180º
C=180º-100º
C=80º

Answer:

</span>a=7;  A=50º
b=7;  B=50º
<span>c=9;  C=80º</span>

8 0
3 years ago
One kilogram is approximately equal to 2.21 pounds. Find the number of pounds in 28 kilograms. Round to the nearest tenth of a p
Lunna [17]

Answer:I got 61.88

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Could u tell me what 60:48 in its simplest form is please
    10·1 answer
  • Which one is steeper
    13·1 answer
  • State whether the following is reasonable or not. Explain your answer. Josefina gave away 130% of her stamp collection.
    8·1 answer
  • Over the last three evenings, Kala received a total of 131 phone calls at the call center. The third evening, she received 4 tim
    10·2 answers
  • Graph the line with slope 8 and y-intercept -8.
    10·1 answer
  • Damon has 5 dimes and some nickels in his pocket worth a total of $1.20. To find the number of nickels Damon has, a student wrot
    10·1 answer
  • Please help me ASAP.
    5·2 answers
  • One particular hotel in the downtown area costs \$90$90dollar sign, 90 a night. An additional 10\, percent tax is added to the o
    5·2 answers
  • If x=7 and y=-3 xy/3 + 2
    11·1 answer
  • Please show the work. 5256÷52, 5624÷46, 756÷36, 2760÷12. It's a lot to do, so I'm making this 40 points.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!