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
erastovalidia [21]
3 years ago
13

the ratio of an equal side of an isosceles triangle to it's base is 3:4 and it's perimeter is 60 cm. find its area.​

Mathematics
1 answer:
Ann [662]3 years ago
5 0

Answer:

160.10 (2 dp.)

Step-by-step explanation:

So when you have ratio questions, similar to this one, you should always add up the parts.

This question actually involves many steps.

We are trying to find the length of all the sides first, we already know that the 3 sides add up to 60cm.

The triangle is made up of 3:3:4, as it has two equal sides and one base. The total parts is 3 + 3 + 4 = 10.

To find how much one part is. we divide the perimeter by the total parts

60/10 = 6

If one part equals 6, then we just multiply by the number of parts to find the entire length, this means that the sides equal 6 x 3 = 18 and the base is

6 x 4 = 24.

Now, we need to find the height in order to find the area of the triangle, to find the height we will be using Pythagoras theorem.

Pythagoras theorem states that a^2 + b^2 = c^2

If we split the triangle in half down the middle, we have a right angle triangle, we know the length of hypotenuse and one side.

The hypotenuse would be one of the equal sides of the isosceles triangle, which is 18cm, and the other side would be half of the base which is 24/2 = 12cm , as we are splitting the isosceles triangle down the middle.

Now we can use the theorem to find the height:

a = height

b = 12

c = 18

Formula:

h^2 + 12^2 = 18^2

rearrange and simplify:

18^2 - 12^2 = h^2

324 - 144 = h^2

180 = h^2

h = root 180 (we will leave this as a surd as it is not a perfect square)

Now that we know the height we can find the area, the formula of a triangle is half x base x height:

1/2 x 24 x root 180

= 160.10 (2 dp.)

Hope this helps,

Cate

You might be interested in
Which ordered pair makes both inequalities true? y > –2x + 3 y < x – 2 On a coordinate plane, 2 straight lines are shown.
ivolga24 [154]

Answer:

(3,0)

Step-by-step explanation:

6 0
2 years ago
Hellppp what statement is true???
miss Akunina [59]
I’m not sure, I think the second
8 0
3 years ago
What is the area of a regular nonagon with 10 cm sides and an apothem if 6cm?
bearhunter [10]

Answer:

The area of the nonagon is 270cm²

Step-by-step explanation:

The area of a regular polygon is given by

=  \frac{1}{2} ap

where 'a' is the apothem and 'p' is the perimeter.

The apothem is a=6cm.

The perimeter is p=9×10=90cm.

We substitute the apothem and the perimeter to get:

=  \frac{1}{2}  \times 6 \times 90 {cm}^{2}

= 270 {cm}^{2}

8 0
3 years ago
Please help me no bs
Nataly_w [17]

Answer:

what do you need help with? and thank you for the points! Once you tell me what you need help with I will write the answer in the comments!

Step-by-step explanation:

3 0
3 years ago
1.name a pair of lines that are perpendicular<br>2.name a pair of line's that appear to be parallel
SSSSS [86.1K]
1) F-J and H-G
2)D-C and F-J
7 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following has the largest value?<br> 1/2 0.09 35%
    8·1 answer
  • A birds nest is 12 feet above the ground. A moles den is 12 inches below the ground. What is the difference in the height of the
    15·1 answer
  • I need to solve for x and I’m confused it’s about angels please help me
    12·1 answer
  • Evaluate the expression for the given value of the variable(s). |4b-4| + |3-b^2| +2b^3; B=2
    15·1 answer
  • Tell whether the statement is true or false. Explain. Help please
    13·1 answer
  • Please solve this ASAP.
    6·1 answer
  • Log(8)a/2. Expand the logarithmic expression.
    10·1 answer
  • Choose an answer and tell me why you chose that :)
    15·1 answer
  • Denise earns $30 an hour. She works 40 hours per week. A. Create and solve an expression to represent how much money Denise earn
    13·2 answers
  • Sam is thinking of retiring from his job after many years of faithful service. during the last 35 years at his job, his annual s
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!