Answer:
x=25 or x=0
Step-by-step explanation:
4x(x−25)=0
Step 1: Simplify both sides of the equation.
4x2−100x=0
For this equation: a=4, b=-100, c=0
4x2+−100x+0=0
Step 2: Use quadratic formula with a=4, b=-100, c=0.
x=−b±√b2−4ac over 2a
x=−(−100)±√(−100)2−4(4)(0) over 2(4)
x=100±√10000 over 8
x=25 or x=0
Let h represent the height of the trapezoid, the perpendicular distance between AB and DC. Then the area of the trapezoid is
Area = (1/2)(AB + DC)·h
We are given a relationship between AB and DC, so we can write
Area = (1/2)(AB + AB/4)·h = (5/8)AB·h
The given dimensions let us determine the area of ∆BCE to be
Area ∆BCE = (1/2)(5 cm)(12 cm) = 30 cm²
The total area of the trapezoid is also the sum of the areas ...
Area = Area ∆BCE + Area ∆ABE + Area ∆DCE
Since AE = 1/3(AD), the perpendicular distance from E to AB will be h/3. The areas of the two smaller triangles can be computed as
Area ∆ABE = (1/2)(AB)·h/3 = (1/6)AB·h
Area ∆DCE = (1/2)(DC)·(2/3)h = (1/2)(AB/4)·(2/3)h = (1/12)AB·h
Putting all of the above into the equation for the total area of the trapezoid, we have
Area = (5/8)AB·h = 30 cm² + (1/6)AB·h + (1/12)AB·h
(5/8 -1/6 -1/12)AB·h = 30 cm²
AB·h = (30 cm²)/(3/8) = 80 cm²
Then the area of the trapezoid is
Area = (5/8)AB·h = (5/8)·80 cm² = 50 cm²
Answer: Congruent Angles
Step-by-step explanation:
Answer:
1100
Step-by-step explanation:
