Answer:
Step-by-step explanation:
Remark
You are going to use the Pythagorean Theorem. The trick is to find the length of the leg making up the base of the triangle.
That base is equal to the difference between the two bases.
Solution
The base of the triangle = 2x + 1 - (x + 3) Remove the brackets.
base = 2x + 1 - x - 3
base = x - 2
Now the height of the trapezoid is also the second leg of the triangle. Apply the Pythagorean Theorem.
c^2 = a^2 + b^2
a = x - 2
b = x + 4
c = 2x
4x^2 = (x - 2)^2 + (x + 4)^2 Expand the brackets
4x^2 = x^2 - 4x + 4 + x^2 + 8x + 16 Collect like terms
4x^2 = 2x^2 + 4x + 20 Subtract the right side from the left.
4x^2 - 2x^2 - 4x - 20 = 0
2x^2 - 4x - 20 = 0 Divide by 2
2x^2/2 - 4x/2 - 20/2 = 0
x^2 - 2x - 10 = 0
x = - b +/- sqrt(b^2 - 4*a*c)/ 2a
a = 1
b = - 2
c = - 10
x = (- -2 + / - sqrt((-2)^2 - 4*(1)*(-10) ) / 2
x = (2 + / - sqrt(4 + 40 ))/2 Only the plus root has any meaning.
x = ( 2 + sqrt(44 ) )/2
x = ( 2 + 2*sqrt(11) ) / 2
x = 1 + sqrt(11)
sqrt(11) = 3.3166
x = 1 + 3.3166
x = 4.3166
Plug in what we know:
Find the cube root of both sides:
![\sf~a=\sqrt[3]{2744}](https://tex.z-dn.net/?f=%5Csf~a%3D%5Csqrt%5B3%5D%7B2744%7D)
Simplify:
The difference between 301 and 134 is 167
What is difference?
Difference in mathematics means subtracting one number from another.
According to the question, we were asked to subtract 134 from 301
301 -134
= 167
Hence the difference between 301 and 134 is 167
Read more on difference here
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1.4 hours
It took a while to get this one, and I must admit, I'm not the best at explaining anything so I'm simply going to leave the answer above to help those who are stuck.
