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In $19-25,$ express each answer in simplest radical form. Check each answer. The lengths of the bases of a trapezoid are $x+10$ and $3 x+2$ and the length of the altitude is 2$x$ . If the area of the trapezoid is $40,$ find the lengths of the bases and of the altitude.

Bases: 12 and 8Altitude: 20

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 2

The Quadratic Formula

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

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discussion. Here we have a chapas oId with two bases. One base is X plus 10 Toby one sex was 10 and B two is equal to three X plus two with a height or altitude of two max. We also know that the area is equal to 40. So we know that to find the area here we have B one plus B two divided by two times the height and this is equal to area. Where they should be written is high. Since we know each of the values here, you know that be one is you could expose 10 and B two's equal to three expose to H is equal to X In the areas of the 40 we consult for X so we have these twos cancel out here in the numerator we have for ex post 12 times X is equal to 40. So for X squared plus 12 x minus 40 is you go to zero dividing everything before we have X squared. Plus three x minus 10 is equal to zero To solve for X, we can use the quadratic formula. You have negative B plus finest the square root O B squared minus four times a times C about a pipe to a. This is equal to negative. Three cost. Minus the square root. So 49 to guarded by two four negative three plus minus seven divided by two So two options are negative. Three plus seven Divided by two, which is equal to two or negative three minus 72 out of my to it is equal to negative five. But because here we're solving for X, which and the height is equal to two times X, we have to make sure that next must be positive because we cannot have a negative height. So that means that acts cannot equal of your five so X is equal to two. Therefore, our bases are equal to two plus 10 which is equal to 12. Three times two plus two. Musical to eight, and the height or altitude is equal to two times two, which is equal to four. So be one is you got 12 be to you go to eight and altitude is equal to four

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