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
Eduardwww [97]
3 years ago
8

An architect wants to draw a rectangle with a diagonal of 13 centimeters. The length of the rectangle is to be 3 centimeters mor

e than triple the width. What dimensions should she make the rectangle?​
Mathematics
1 answer:
butalik [34]3 years ago
5 0

Answer:

The rectangle is 3.2 cm by 12.6 cm

Step-by-step explanation:

See attached image for a diagram.

Choose <em>w</em> to represent the width because the length is described by referring to the width:  it's 3 more than (add 3) triple (multiplied by 3) the width.

Length = 3w + 3

The diagonal forms two right triangles, each with leg = <em>w</em>, other leg = 3<em>w</em> + 3, hypotenuse  =  13.

The Pythagorean Theorem says (\text{leg})^2+(\text{leg})^2=(\text{hypotenuse})^2 so

w^2+(3w+3)^2=13^2\\\\w^2+9w^2+18w+9=169\\\\10w^2+18w-160=0\\\\5w^2+9w-80=0\\

Now solve using the Quadratic Formula with a=5,\,b=9,\,c=-80.

w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\w=\frac{-9\pm\sqrt{81+1600}}{10}\\\\w=\frac{-9\pm\sqrt{1681}}{10}\\\\w=\frac{-9\pm41}{10}\\\\w=-5\text{ or }w=3.2

The negative root makes no sense as a distance, so the width of the rectangle is 3.2 cm. The length is 3(3.2) + 3 = 12.6 cm.

You might be interested in
27x^3−64divided by3x−4
Vitek1552 [10]

Since the denominator of any fraction can’t =0, then 3x-4 can’t = 0. What will make that 0? Let’s see: 3x-4=0. 3x=4. X= 4/3. Everything else will work!


5 0
3 years ago
Read 2 more answers
How big is the earth
melomori [17]
The 4th largest planet
7 0
3 years ago
Factor x^2+3xy+2y^2+4x+7y+3
Aleksandr-060686 [28]
3xy(x+4)(2y+7)(xy+1) is what I got
4 0
3 years ago
timothy creates digital art prints for his art show.in 1 day he created 8 diffrent art prints.which equation best represents y,t
Ghella [55]

Answer:

Step-by-step explanation:

3 0
2 years ago
If you guys want me to join y’all’s class in like zoom then tell me your class id and password.
sammy [17]

Answer:

You cant join mine. Mine has strict rules and c rap sign up with a email and stuff.

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−1, −1)?
    5·1 answer
  • Find all the zeroes of the equation. -3x4+27x2+1200=0 I need to learn how to do it! Just not the answer please
    12·2 answers
  • your local radio station is having their yearly MP3 player and concert giveaway. For one minute every 5th caller will win an MP3
    14·2 answers
  • Express the given cartesian co-ordinate as polar co-ordinate correct to 2 decimal places a.(3,5) b.(6.18,2.35) c.(-2,4) d.(9.6,-
    9·1 answer
  • A newsletter publisher believes that 71q% of their readers own a personal computer. Is there sufficient evidence at the 0.010.01
    10·1 answer
  • HELP ASAP!!!!
    7·2 answers
  • During his first three months with the Houston Astros, Yordan Álvarez's batting average was represented by three hundred sevente
    12·1 answer
  • The cost of a holiday is £2400
    9·1 answer
  • What is the image of (2, 1) after a reflection over the x-axis?
    7·1 answer
  • What's Gold To Me Personal Narrative
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!