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]
2 years 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]2 years 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
What is the average of 3.28+6.90+5.30+12.00+4.77
schepotkina [342]
The answer should be 32.25
6 0
3 years ago
The solution to the inequality 5x - 4 > 21 is represented by which number line?
andrew-mc [135]

Answer:

Step-by-step explanation:

Start with the given inequality and solve it for x.

First, add 4 to both sides:  5x > 25

Next, divide both sides by 5:  x > 5

The solution (set) is x > 5.

7 0
3 years ago
What is this ?????? plz helpppp
gogolik [260]

Answer:

The baker uses 15 cups of cereal for 10 cups of marshmallows

Step-by-step explanation:

The proportion 6:4 has to stay true in the answer, so both numbers have to be multiplied by the same number

6 x 2.5 = 15

4 x 2.5 = 15

both numbers were multiplied by the same number in this answer and it is the only answer that stays true to the ratio

6 0
3 years ago
Suppose that $1,000 is deposited into an account that yields
Lana71 [14]
ANSWER : $1,215.51

P= Principal = $1000
R= rate = 5% = 0.05
N= number or periods in 1 year (1 time pre year)
T= time expressed in years = 4 years

A= P (1 + r/n) nxt
= 1,000 (1+ 0.05/1) 1x4
= 1,215.51

6 0
3 years ago
Which function has zeros at x = -2 and x = 5?
riadik2000 [5.3K]

Answer:

<em>f(x)=x²-3x-10</em>

Step-by-step explanation:

\begin{gathered}f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5\end{gathered}

f(x)=x

2

−3x−10

tofindxinterceptorzerosubstitutef(x)=0

0=x

2

−3x−10

x

2

−3x−10=0

x

2

+2x−5x−10=0

x(x+2)−5x−10=0

x(x+2)−5(x+2)=0

(x+2).(x−5)=0

x+2=0

x−5=0

x=−2

x=5

therefore the zeros of the equation are x₁=-2,x₂=5

3 0
1 year ago
Other questions:
  • How to write a standard form equation with an undefined slope?
    5·1 answer
  • Which shape is both a rectangle and a square?<br> please help i’ll rate you brainliest
    5·2 answers
  • On a map, the scale shown is 1 inch: 20 miles. If a city is 900 square miles, what is the area of the city on the map?
    6·1 answer
  • Help me pls 63 dived 3,448
    13·2 answers
  • I’ll mark as BRANLIEST!!
    5·1 answer
  • Mathematical statements into logical statements with nested quantifiers. About Translate each of the following English statement
    8·1 answer
  • Question 15
    7·2 answers
  • 8) Find the midpoint of the equation y = 4x + 6 between the x-intercepts and the y-intercepts.​
    9·1 answer
  • HELP<br> WRITE AS EQUATION IR EXPRESSION<br> 500 decreased by sum of a number and 2 is 300
    5·1 answer
  • Earned 60 points on his last test if there were 75 possible points what was his percent grade ?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!