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
Levart [38]
1 year ago
15

Find the base of an isosceles triangle whose area is 60 cm² and the length of one of its equal sides is 13 cm. ​

Mathematics
1 answer:
Kobotan [32]1 year ago
4 0

Answer:

Base = 24 cm or 10cm

Step-by-step explanation:

REMEMBER:
An isosceles triangle ABC with base BC = ‘b' & height AD = ‘h' & its equal sides =13 cm & area = 60 cm²

Using the formulas

A=\frac{bh_b}{2}

h_b=\sqrt{a^2-\frac{b^2}{4} }

There are 2 solutions for b

b=2\sqrt{2}   \frac{A}{\sqrt{a^2+\sqrt{a^4-4A^2} } } =2*\sqrt{2} *\frac{60}{\sqrt{13^2+\sqrt{13^4-4*60^2} } } ≈ 10cmb=2\sqrt{2}   \frac{A}{\sqrt{a^2+\sqrt{a^4-4A^2} } } =2*\sqrt{2} *\frac{60}{\sqrt{13^2-\sqrt{13^4-4*60^2} } }=24cm

Less complex:

Area of a triangle = 1/2 * b * h = 60

=> h = 120/b

In right triangle ABD

13² = h² + b² /4 ( by Pythagoras law)

=>169 = 120²/b² + b²/4

=>676 b² = 57600 + b^4

=> b^4 - 676 b² + 57600 = 0

=> b² = 676 +- √(676² - 4*57600) / 2

=> b²= 676 +- √(226576) /2

=> b² = (676 +- 476 )/2

=> b² = 1152/2 , 200 /2

=> b² = 576 , 100

=> b = 24, 10

So, Base = 24 cm or 10cm

You might be interested in
Jeremy drew a polygon with four right angles and four sides with the same length name all the polygons that he have done
erik [133]

The most-specific name for such a polygon is square.

It can also be called a <em>rectangle</em>, <em>rhombus</em>, <em>parallelogram</em>, or <em>quadrilateral</em>.

6 0
3 years ago
PLZ HELPPPP I NEED HELP ASPA
kakasveta [241]

Idk but you have roblox in your hot bar? FRIEND ME PLS!!!!!!

7 0
3 years ago
Read 2 more answers
Suppose you want to create a set of weights so that any object with an integer weight from 1 to 40 pounds can be balanced on a t
Archy [21]

Answer:

You need 4 weights, and the weights are 1; 3; 9 and 27.

Step-by-step explanation:

<em>Since the scale has two plates, we can place weights on either side and also the object so it can be balanced. </em>

This is a key part of the problem, it's not only on the other side of the scale, but on both sides.

Let's do the math now.

If i get two weights, 1 and 3. I can form this combinations.

Object of 1lb = 1

Object of 2lb + 1 weight = 3 weight.

Object of 3lb = 3 weight

Object of 4lb = 1 weight + 3 weight.

So what if i want to add the next weight and that weight to add me the maximum amount of objects. The weight would have to have a difference with the last object plus one. So if i grab 9. 9 minus 4 is 5. And that is a difference with the last object plus 1.

With a weight of 9, now i can add all the integers up to 13lb.

And the next step? Lets add one more. Keeping the last rule, the weight would have to have a difference with the last object plus one. So if i grab 27, 27 minus 13 is 14. And that is a difference witht the last object plus 1.

The sum of all the weights adds up to 40 pounds. And i can balance any integer in the middle.

The formula we are using is p – n = n + 1

Where p is the new weight. and n is the last object we weighted. And the sum of the weights goes up to the last object we can place on the scale, and in this case is 40.

4 0
3 years ago
Determine how long it will take for $4000 to quadruple in a bank account earning 3.57% interest compounded continuously. Round t
tankabanditka [31]

Answer:

12 months, so 1 year

Step-by-step explanation:

5 0
2 years ago
Find the slope of the line that passes through the given points (5,-1), (-7,2)
soldier1979 [14.2K]

Answer:

4y = -m-1 bcoz u use the formula y-y1 = (y2-y1/x2-x1) times (x-x1)

7 0
2 years ago
Other questions:
  • April is randomly choosing five CDs to bring in her car from the following: 6 pop CDs, 8 rock CDs, and 10 R&amp;B CDs. What is t
    5·2 answers
  • I need to Find the value of x
    8·1 answer
  • Solve. Write your answer in simplest form.
    11·2 answers
  • Which of the following equations corresponds to the graph below?
    5·2 answers
  • Pls help! question is on picture, will mark brainlyest if its right
    9·1 answer
  • What is -3/5 as a decimal​
    9·2 answers
  • SOMEONE PLEASE HELP ME THIS IS ALMOST DUE AND I NEED THE RIGHT ANSWER PLZ!!!
    14·1 answer
  • The graph shown matches which quadratic equation?<br> A<br> yox. 1<br> yox-1)?<br> D
    13·2 answers
  • (algebra 2)
    7·1 answer
  • Bella and her sisters have 8 popsicles they have to fig rout how to split them what is the answer do we have to multiply, divide
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!