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
dalvyx [7]
3 years ago
15

The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

. Find the dimensions of the triangle.
Mathematics
1 answer:
snow_tiger [21]3 years ago
5 0

Answer:

Hypotenuse = 25cm

Opposite = 24cm

Adjacent = 7cm

Step-by-step explanation:

Represent:

  • The opposite with a
  • The adjacent with b
  • The hypotenuse with c

Given that:

c = 1 + a

c = 4 + 3b

Required

Solve for a, b and c

c = c

So, we have:

1 + a = 4 + 3b

Subtract 1 from both sides

a = 4 -1 + 3b

a = 3 + 3b

Apply Pythagoras Theorem

c^2 = a^2 + b^2

Substitute 3 + 3b for a and 4 + 3b for c

(4 + 3b)^2 = (3 + 3b)^2 + b^2

Open brackets

16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2

16 + 24b+9b^2 = 9 + 18b+10b^2

Collect Like Terms

10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0

b^2 - 6b -7 = 0

Expand

b^2 +b-7b-7=0

Factorize:

b(b+1)-7(b+1) =0

(b-7)(b+1) = 0

Split:

b - 7 = 0\ or\ b+1=0

b = 7\ or\ b=-1

But the adjacent of a triangle can't have a negative measurement.

So:

b = 7

Recall that:

c = 4 + 3b

a = 3 + 3b

Substitute 7 for b in the above expressions

c = 4 + 3 * 7

c = 4 + 21

c = 25

a = 3 + 3 * 7

a = 3 + 21

a = 24

Hence, the dimensions of the triangle are:

Hypotenuse = 25cm

Opposite = 24cm

Adjacent = 7cm

You might be interested in
Help am stuckkkkk please help​
Otrada [13]

Step-by-step explanation:

it is a box or prism.

the volume is simply

length × width × height

in our case

8m × 6m × 5m = 240 m³

doubled dimensions means

16m × 12m × 10m = 1920 m³

the difference is

1920 - 240 = 1680 m³

we could have gotten the new volume also based on the original volume :

2×8m × 2×6m × 2×5m = 8m×6m×5m × 2×2×2 =

= the original volume (240 m³) × 8 = 1920 m³

3 0
2 years ago
What is the circumference of a circle with an area of 50.24? Use 3.14 for pi.
kow [346]

Answer:

The answer is 200.96 cm^2.

2*3.14*r=50.24

=>r=50.24/6.28

=>r=8 cm

Thus area = 3.14*r*r

= 3.14*8*8

=200.96 cm^2

Step-by-step explanation:

4 0
3 years ago
Filled with jelly beans. If the jar has a<br> 15% are purple How many purple beans are they ?
Rzqust [24]

Answer:

147 purple jelly beans

Step-by-step explanation:

15% of 980 is 147

8 0
3 years ago
Given that APOR is similar to APTS, what is the value of x?
marusya05 [52]

Answer:

D.

Step-by-step explanation:

8 0
2 years ago
15. Find M /_ B.
aliina [53]

Answer:

m∠B=79°

Step-by-step explanation:

∠A +∠B+∠C+∠D=360°

14x-11+8x+7+5x+18+10x+13=360°

37x+27=360°

37x=333

x=9

so,

m∠B=8x+9

m∠B=8×9+7

m∠B=79°

Hope it helps!

7 0
2 years ago
Read 2 more answers
Other questions:
  • X+2y=3<br> x-y=6<br> x=? y=?
    11·2 answers
  • Answer number 15 plz!. Plz do this ASAP!!!!!!!!!
    15·2 answers
  • Janice rode her bike at an average of 12 miles per hour for 3 hours. Renee rode her bike at an average of 14 miles per hour for
    7·2 answers
  • What is the equation of the line parellel to line L that passes through point (3, 3)?
    7·1 answer
  • Please help asap!! no trolls
    14·2 answers
  • Gun ownership Concerned about recent incidence of gun violence, a public interest group conducts a poll of 850 randomly selected
    8·1 answer
  • There are less than 50 students in this class. Today, only 97.5% of the class is here. How many students are in this class?
    9·2 answers
  • .
    7·1 answer
  • Asap 50 points! <br>-3xy = what when x=5 and y= -6<br>answers : <br>-90<br>90<br>-33<br>33​
    8·2 answers
  • Plss help ASAP plss GIVING BRAILIEST​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!