The area will be equal to Area = (28)(21) / 2 = 294 square inches.
<h3>What is the area?</h3>
To determine the area of a triangle, we calculate one half of the product of the base and the height of the triangle so we need data on its base and its height. We are given the following:
Hypotenuse = 7 + base = 14 + height
Perimeter = 84 inches
The perimeter of the triangle is equal to the sum of the three sides of the triangle which are the height, base and hypotenuse. So,
Perimeter = height + base + hypotenuse = 84
We let x = height and y = base. We calculate area as follows:
84 = x + y + (7 + y)
77 = x + 2y
x = 77 -2y
The Hypotenuse is related to the other sides by the Pythagorean theorem.
Hypotenuse^2 = (x^2 + y^2)
(14 + x)^2 = x^2 + y^2
(14 + (77-2y))^2 = (77-2y)^2 + y^2
(91-2y)^2 = (77-2y)^2 + y^2
Solving for y and x
y = 28
x = 21
Area = (28)(21) / 2 = 294 square inches
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All you need to do is plug 19 in for x and solve.
f(19) = 3/(19+2) - sqrt(19-3) = 1/7 - sqrt(16)= 1/7 - 4
The answer is -3.8571 or as a fraction -27/7
If you are looking to find the discounted price, you would multiply 89 by .15 to get 13.35. This is the amount that is taken off,o r 15 percent of 89. Subtract 13.35 from 89 to get 75.65 as the discounted price.
If you draw a diagonal from upper left to lower right, you divide the figure into two triangles. One is a 3-4-5 right triangle (with area = (1/2)*3*4 = 6). The other is a 5-5-4 isosceles triangle.
The altitude of the isosceles triangle (upper left vertex to side 4) can be found from the Pythagorean theorem as
.. altitude = √(5^2 -2^2) = √21
So, the area of the isosceles triangle is
.. (1/2)*4*√21 = 2√21
The sum of the areas of the two triangles matches selection C.
X= 8
Y= -7
If you use elimination:
–3y–4x=–11
3y–5x=–61
Add the two equations and get
–9x=–72
Divide by –9 on both sides
X=8
Substitute 8 in for x
–3y–4(8)=–11
Simplify
–3y–32=–11
Add 32 on both sides
–3y=21
Divide by –3 on both sides
Y=–7