An isosceles triangle is to be drawn with its two equal sides of length 10. What is the maximum possible area of the triangle?
Answers
Since an isosceles triangle has two equal sides, if the triangle is split in half vertically, the length of the base on each side is:
12
c
m
÷
2
=
6
c
m
We can then use the Pythagorean theorem to find the height of the triangle.
The formula for the Pythagorean theorem is:
a
2
+
b
2
=
c
2
To solve for the height, substitute your known values into the equation and solve for
a
:
where:
a
= height
b
= base
c
= hypotenuse
a
2
+
b
2
=
c
2
a
2
=
c
2
−
b
2
a
2
=
(
10
)
2
−
(
6
)
2
a
2
=
(
100
)
−
(
36
)
a
2
=
64
a
=
√
64
a
=
8
Now that we have our known values, substitute the following into the formula for area of a triangle:
b
a
s
e
=
12
c
m
h
e
i
g
h
t
=
8
c
m
A
r
e
a
=
b
a
s
e
⋅
h
e
i
g
h
t
2
A
r
e
a
=
(
12
)
⋅
(
8
)
2
A
r
e
a
=
96
2
A
r
e
a
=
48
∴
, the area is
48
c
m
2
.
Related Questions
Answer the following 3 questions CORRECTLY I will know if this is wrong. I WILL REPORT ANY INCORRECT ANSWERS!Criteria for getting brainliest and not getting reported:- Show work- Explain if you can't show work why this answer is correct.- And make sure not to post random answers points are taken away when you are reported so don't think about answering it if you want only just want points to move up.1. What is the quotient in the expression c = ?A) B) dC) 45D) c2. The grocery store has 8 snack bags. There are 3 bagels and 4 muffins in each bag. How would you calculate the total number of muffins?A) Multiply 8 by the sum of 3 and 4B) Multiply 8 by 3C) Multiply 8 by 4D) Add, 3, 4, 83. The box holding the instruments for science class is square. The box measures 15 inches by 15 inches and is 2 inches deep. This means that the volume of the box is “15 times 15 times 2” cubic inches. Which of the following formulas is an equivalent expression for “15 times 15 times 2”?A) (15 x 2)^2B) 15^2 x 2C) 2^2 x 15D) (15 x 15)^2 x 2
Add the polynomials (7x3−2x2−12)+(−3x3−8x2+10x)
The function f(t) = 4t^2 − 8t + 6 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)^2 + k, where a, h, and k are integers, and interpret the vertex of f(t).A - f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 3 meters from the groundB - f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 1 meter from the groundC - f(t) = 4(t − 1)^2 + 2; the minimum height of the roller coaster is 2 meters from the groundD - f(t) = 4(t − 1)^2 + 2; the minimum height of the roller coaster is 1 meter from the ground
Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes.Let x represent the number of quick washes and let y represent the number of premium washes. Which system of linear equations represents the situation? 5x + 8y = 775 and x + y =125 5x – 8y = 125 and x + y = 775 5x + 8y = 775 and x – y = 125 5x – 8y = 125 and x – y = 775
x - 3 is a factor of P(x) = x^3 – 7x² +15x-9
A. True
B. False
Answers
Explanation-
Let p(x) = x^3 – 7x^2 – 15x – 9
For checking that (x – 3) is a factor of p(x), we find : p(3)
p(3) = (3)^3 – 7(3)^2 + 15(3) – 9
= 27 – 63 + 45 – 9
= 72 – 72
= 0
Hence, (x – 3) is a factor of p(x).
By division of p(x) by x – 3, we get the quotient
= x^2 – 4x + 3
∴ x^3 – 7x^2 + 15x – 9
= (x – 3)(x^2 – 4x + 3)
= (x – 3)(x – 3)(x – 1)
= (x – 3)^2(x – 1)
Answers
We know that the Pythagorean Theorem is the following:
where c is the hypotenuse (the side opposite the right angle), and a and b are the legs of the triangle.
To solve, we just have to input what we know. The two legs of the triangle are 60 and 100, so we just have to plug these values in and solve.
So we know that the distance from one corner of the playing field to the opposite corner is the square root of 13,600 yards.
When we plug this into a calculator, we get
which, when rounded up to the nearest whole number, is 117.
The approximate distance from one corner of the soccer field to the opposite corner is 117 yards.
Hope that helped! =)
Answers
They want us to find the volume of model 413S in ft³
This isnt tough!
change the side measurements from Inches to Feet
12 in = 1 ft
so therefore:
24 in = 2 ft
72 in = 6 ft
18 in = 1.5 ft
Volume of a cuboid is:
Area of base × height of cuboid
V = 2 ft × 6 ft ×1.5 ft
= 18 ft³
Volume of the cabinet (Model 413S) is 18 ft³
So, by this statement we got to know that the model is in cuboid shape.
Hence, its volume will be (length×width×height) cubic feet.
Answers
Answer:
c
Step-by-step explanation:The answer is c which is 23%
Answers
Answer:
18 I think
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Reagan brought 2 caramel brownies.
Solve using a proportion.
=
You're trying to find how many brownies he brought were caramel. We know Reagan brought a total of 20 brownies. Therefore since you don't know how many caramel brownies he brought, the fraction would be ?/20. Next, you know he brought brownies in which 10% were caramel. In proportions, the denominator would be 100% since that is the total percentage. Therefore, the proportion would be 10%/100%. Now we just have to cross multiply.
Proportion:
=
10 x 20 = 200
200/100= 2
Thus, Reagan brought 2 caramel brownies.
Answers
m 2 = V 2 * d
Both tetrahedrons have the same density.
V = 1/3 * a²√3/4 * h
V 1 = 1/3 * 1² * √3 / 4 * √2 / √3 = √2 / 12 cm³
V 2 = 1/3 * 3²√3 /4 * √6 = 9√2 / 4 cm³
m 1 : m 2 = √2 /12 : 9√2/4
m 1 * 9√2 / 4 = m 2 * √2 / 12
m 1 = m 2 / 27
m 1 + m 2 = 100 g
m 2 / 27 + m 2 = 100 g / * 27
m 2 + 27 m 2 = 2700
28 m 2 = 2700
m 2 = 2700 : 28
m 2 = 96.42 g
Answer:
The weight of the bigger tetrahedron is 96.42 g.