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
katen-ka-za [31]
3 years ago
10

The base of a triangle exceeds the height by 7 centimeters. If the area is 400 square centimeters, find the length of the base a

nd the height of the triangle.
Mathematics
1 answer:
zvonat [6]3 years ago
8 0

Answer:

Base = 32 cm

Height = 25 cm

Step-by-step explanation:

Area of a triangle can be calculated as:

Area = \frac{1}{2}\times Base \times Height

We are given that the base of triangle exceeds the height by 7 cm. This can be expressed in an equation form as:

Base = Height + 7

Lets use B to represent base and H to represent height

B = H + 7

The equation of area can be stated as:

Area=\frac{1}{2}bh\\\\ Area=\frac{1}{2}(h+7)(h)\\\\ 400=\frac{1}{2}h(h+7)\\\\ 800=h^{2}+7h\\\\ h^{2}+7h-800=0

This is a quadratic equation which can be solved using a quadratic equation as shown below:

h=\frac{-7+-\sqrt{49-4(1)(-800)} }{2(1)} \\\\ h=\frac{-7+-57}{2}\\\\h=-32,25

Since the height cannot be negative, we'll consider the positive value only i.e height is equal to 25 cm.

Therefore, the length of base will be 25 + 7 = 32 cm.

You might be interested in
an urn contains twenty chips, numbered 1 through 20. two are drawn at random simultaneously (without replacement). what is the p
ElenaW [278]

The probability of the numbers on the two chips differing by more than two are 0.805.

<h3>What is probability? </h3>

The study of numerical representations of the possibility of an event occurring or a proposition being true is known as probability. A probability is a number between 0 and 1, where 0 denotes impossibility and 1 denotes certainty.

Given that,

Urn is composed of twenty chips, numbered one through twenty.

Two are drawn at random simultaneously.

The probability that the numbers on the two chips deviate by greater than two.

Probability = 20 x 20 - 20

Probability = 400 – 20

Probability = 380 total possible outcomes for 20 outcomes.

In the first and last rows, we can also observe that there are 20-3 = 17 choices with a difference greater than 2.

In the second and next-to-last rows, there are 20-4 =16 possibilities for a difference greater than 2.

As a result, the total is 2(17) + 2(16) + 2(15) = 306

Probability = Favorable outcomes/Total number of outcomes

Probability = 306/380

Probability = 153/190

Probability = 0.805

The probability of the values on the two chips varying by more than two is 0.805.

To know more about probability, visit:

brainly.com/question/11234923

#SPJ4

6 0
1 year ago
Can someone plz help me find the answer to 2x=4 y-16. and 2x-y=-7
telo118 [61]

Answer:

So, y = 2x + 7;

Then, 2x = 4( 2x + 7 ) - 16;

2x = 8x + 28 - 16;

2x = 8x + 12;

- 6x = 12;

x = - 2;

Then, y = 2· (-2) + 7;

y = - 4 + 7;

y = 3.

Step-by-step explanation:


8 0
3 years ago
HELP ONLY ANSWER QUESTION 10. THANKS
swat32
X - 5 = x^2

i) 0 - 5 = -5^2 = 25

ii) 4 - 5 = -1^2 = 1

iii) -4 - 5 = -9^2 = 81
5 0
3 years ago
Can someone please do 1,2 and 3 please
jok3333 [9.3K]

1. x=−1 or x=−5

2. x=9 or x=−15

3.x=3 or x=−3

3 0
3 years ago
The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A
aalyn [17]

Answer:

.

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • If vector u = (5, 3) and vector v = (-1, 4), what is the component form of vector u + v?
    9·1 answer
  • Two die are rolled simultaneously. what is the probability of getting a sum of at least 5?
    13·1 answer
  • Earning a 6% pay increase to current $62,900 annual salary
    9·1 answer
  • Need help on 16 please!!!!!!!
    15·2 answers
  • G(n)=3n^3-5 h(n)=2n-5 find(g+h)(2)
    6·1 answer
  • Pamela's age is two times Jiri's age. The sum of their ages is 84. What is Jiri's age?
    15·1 answer
  • The straight-line L has equation 2x + y = 8. Find the gradient of L.<br><br>PLEASE HELP !!
    9·1 answer
  • A triangle has one side that is 5 inches long and another that is 7 inches long. How many different lengths, in inches,are possi
    15·1 answer
  • If the solutions of p(x)=0 are -14 and 11, which function could be p?
    11·1 answer
  • In the diagram, is parallel to. Also, is drawn such that the length of is half the length of. If sin A = 0.5, then what is sin E
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!