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
Maru [420]
3 years ago
11

The base of a triangle is nine centimeters longer than the perpendicular height. If the area of the triangle is 180 square centi

meters, what is the length of the base, in centimeters?
Mathematics
1 answer:
Rom4ik [11]3 years ago
7 0

Answer:

<em>The base is 24 cm long.</em>

Step-by-step explanation:

<u>Equations</u>

Let's call

b= base of the triangle

h=height of the triangle

The base is 9 cm longer than the height, thus:

b = h + 9

The area of the triangle is:

\displaystyle A=\frac{bh}{2}

\displaystyle A=\frac{(h+9)h}{2}

And its value is 180:

\displaystyle \frac{(h+9)h}{2}=180

Multiplying by 2:

(h+9)h=360

Operating:

h^2+9h-360=0

Factoring:

(h-15)(h+24)=0

The only valid positive solution is:

h = 15 cm

And b = h + 9 = 24

b = 24 cm

The base is 24 cm long.

You might be interested in
Taylor surveys students in one grade level who own at least one pet. She finds that 50% of the students surveyed own 2 pets, 3 s
Llana [10]
First, we need to work out the total number of students who were being surveyed.

We know that half of the students has two pets. The rest of the students make up the other half. So, we have 3 students + 2 students + 8 students = 13 students that make half of the sample population

That means total number of students being surveyed is 13+13=26 students

Then we work out the probability
P(One pet) = 8/26 = 4/13
P(Two pets) = 1/2
P(Three pets) = 3/26
P( Four pets) = 2/26 = 1/13

The probability distribution is shown in the table below. Let x be the number of pets and P(X=x) is the probability of owning the number of pets


3 0
3 years ago
Read 2 more answers
Surface area of this right prism
Sphinxa [80]

\qquad\qquad\huge\underline{{\sf Answer}}

\textsf{Let's calculate the surface area of given right prism}

\textbf{Area of Triangles :}

  • \sf{\dfrac{1}{2}\cdot 16\cdot 12}

  • \sf{8×12}

  • \sf96 \:  \: cm {}^{2}

\textsf{Since there are two triangles, }

\textsf{Area of Triangles = 96 × 2 = 192 cm²}

\textbf{Now, calculate the Areas of rectangles :}

  • \textsf{Area - 1 = 12 × 10 = 120 cm²}

  • \textsf{Area - 2 = 16 × 10 = 160 cm²}

  • \textsf{Area - 3 = 20 × 10 = 200 cm²}

\textsf{Now add them all :}

  • \textsf{120 + 160 + 200 + 192}

  • \textsf{672 cm²}

7 0
2 years ago
Read 2 more answers
Elizabeth is spinning a spinner with 5 equal sized sections. The sections are numbered 1, 1, 2, 2, 4. Which statement about the
Vinil7 [7]

Answer:

its d

Step-by-step explanation:

the options can be eliminated by using common sense.

8 0
3 years ago
Read 2 more answers
Mary owes her mom $4.50. She borrows $2.17 more from her mom. Which expression shows how to determine the amount, in dollars, Ma
HACTEHA [7]

Answer:

The answer is 4.50+2.17=6.67, which is the amount she owes her mother. Hope this helps!

7 0
3 years ago
Read 2 more answers
This morning,Austin's car had 29.04 gallons of fuel. Now,1.9 gallons are left. How much fuel did Austin use?
Nikitich [7]

Answer:

27.14 gallons

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • Buenas tardes
    11·1 answer
  • What are 10 duties of a police without coping and pasting
    7·1 answer
  • Find the circumference of the circle to the nearest 10th use 3.14 the radius is 25
    14·1 answer
  • I need help please???
    10·1 answer
  • Choose all the numbers that are common multiples of 4 and 5.
    5·2 answers
  • Help someone please​
    15·1 answer
  • Pls help me with this math question pls Pls​
    9·2 answers
  • Lynn is tracking the progress of her plant's growth. Currently the plant is 11 The plant grows 1.2 cm per day. Find an equation
    8·2 answers
  • Below are two regular polygons. Calculate the value of angle a.​
    7·1 answer
  • I’m begging!! please someone help me with this
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!