Which expression is equivalent to StartFraction 2 a + 1 Over 10 a minus 5 Endfraction divided by StartFraction 10 a Over 4 a squ
1 answer:
Answer:
Step-by-step explanation:
Given
Required
Find the equivalent
We start by changing the / to *
Factorize 10a - 5
Expand 4a² - 1
Express (2a)² - 1² as a difference of two squares
Difference of two squares is such that:
The expression becomes
Combine both fractions to form a single fraction
Divide the numerator and denominator by 2a - 1
Simplify the numerator
Hence,
=
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Call the point of intersection of the diagonals point X.
Each base is the hypotenuse of an isosceles right triangle whose sides are the diagonals and whose 90° angle is at X. The altitude of that triangle (⊥ distance to the base from X) is half the length of the hypotenuse. Then the height of the trapezoid is half the sum of the base lengths.
The area of the trapezoid is the product of the height and half the sum of the base lengths, hence is the square of half the sum of the base lengths.
... Area = ((16 cm +30 cm)/2)² = (23 cm)² = 529 cm²
