Find the area of an isosceles triangle with perimeter of 40 feet and a base of 12 feet. Round to the nearest whole number.
1 answer:
Answer: 76 ft2
Step-by-step explanation:
Perimeter = 2 side length +base length
40 = 2s +12
Solving for s:
40-12 =2s
28 =2s
28/2=s
14ft =side
Since the line which bisects and isosceles triangles is at a right angle to the base we can use the Pythagorean Theorem to find the height (see attachment)
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case 14) and a and b are the other sides. (Base divided by 2 is one side, the other side is the height)
Replacing with the values given:
14^2= 6^2 + x^2
196 = 36 + x^2
196-36 = x^2
160 = x^2
√160 = x
x = 12.64 (height)
Area of an isosceles triangle = 1/2 x base x height
A = 1/2 x 12 x 12.64 = 76 ft2
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Answer:
The set of polynomial is Linearly Independent.
Step-by-step explanation:
Given - {f(x) =7 + x, g(x) = 7 +x^2, h(x)=7 - x + x^2} in P^2
To find - Test the set of polynomials for linear independence.
Definition used -
A set of n vectors of length n is linearly independent if the matrix with these vectors as columns has a non-zero determinant.
The set is dependent if the determinant is zero.
Solution -
Given that,
f(x) =7 + x,
g(x) = 7 +x^2,
h(x)=7 - x + x^2
Now,
We can also write them as
f(x) = 7 + 1.x + 0.x²
g(x) = 7 + 0.x + 1.x²
h(x) = 7 - 1.x + 1.x²
Now,
The coefficient matrix becomes
A =
Now,
Det(A) = 7(0 + 1) - 1(7 - 7) + 0
= 7(1) - 1(0)
= 7 - 0 = 7
⇒Det(A) = 7 ≠ 0
As the determinant is non- zero ,
So, The set of polynomial is Linearly Independent.