Answer:
Step-by-step explanation:
Let the height = h
Let the base = 4h + 7
Area of a triangle = 1/2 * b * h
Area = 93 square inches
1/2 * (4h + 7)* h = 93 Multiply both sides by 2
(4h + 7) * h = 93*2
(4h + 7)*h = 186 Remove the brackets
4h^2 + 7h = 186 Subtract 186 from both sides.
4h^2 + 7h - 186 = 0
Use the quadratic formula to solve
a = 4
b = 7
c = - 186
x1 = (-7 + sqrt(7^2 - 4*4*(-186) ) /2*4
x1 = (-7 + sqrt(49 - 16*(-186)) / 8
x1 = (-7 + sqrt(49 + 2976)) / 8
x1 = (-7 + sqrt(3025)) / 8
x1 = (-7 +55 ) / 8
x1 = (48)/8
x1 = 6
There is another root, but it has to be minus and therefore cannot be used as a length. x2 = - 7.75
h = 6
b = 4*6 + 7 = 31
Check
Area = 1/2 * b * h
Area = 1/2 * 31 * 6
Area = 1/2 *186
Area = 93 which is what we were given so the answer is correct.
Circumference = 2 x pi x radius
27 in = 2 x 3.14 x radius
Solve for the radius
Answer: 34/25
Step-by-step explanation:
(136÷4)(100÷4) = 34/25 when reduced to the simplest form. As the numerator is greater than the denominator, we have an IMPROPER fraction,
Parallelograms and trapezoids always do.
(Note: "Parallelograms" includes rectangles, squares, and rhombussesses.)
Any polygon with more than 4 sides <u>can</u> have at least one pair of parallel sides,
but it's not guaranteed.
This should be recognized as the difference of perfect squares which is of the form:
(a^2-b^2) and the difference of squares always factors to:
(a-b)(a+b) in this case:
(3x-8)(3x+8)
