The equation below shows the area of a trapezoid, A, with a height of 9 cm and one base 35 cm.

A = 9 over 2(b + 35)

Which of the following formulas correctly solves for the other base, b?

b = 2A over 9 + 35
b = 2 multiplied by A over 9 − 35
b = 2 multiplied by A plus 35, all over 9
b = 2 multiplied by A minus 35, all over 9

Question

29-08-2022
Mathematics

Answered

The equation below shows the area of a trapezoid, A, with a height of 9 cm and one base 35 cm.

A = 9 over 2(b + 35)

Which of the following formulas correctly solves for the other base, b?

b = 2A over 9 + 35
b = 2 multiplied by A over 9 − 35
b = 2 multiplied by A plus 35, all over 9
b = 2 multiplied by A minus 35, all over 9

Answer :

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xero099 xero099 · Answer 1 · 2022-08-31T08:49:06-04:00

The resulting expression for the base of the trapezoid is b = (2 / 9) · A - 35. (Correct choice: B)

What is the formula of the base of the trapezoid in terms of the area of a trapezoid?

In this problem we find a formula for the area of the trapezoid in terms of the length of the base and we must use algebraic procedures to derive an expression of the length of the base of the trapezoid:

A = (9 / 2) · (b + 35) Given

A = (9 / 2) · b + (9 / 2) · 35 Distributive property

A = (9 / 2) · b + 315 / 2 Definition of multiplication

A - 315 / 2 = (9 / 2) · b Compatibility with addition / Existence of the additive inverse / Modulative property

b = (2 / 9) · (A - 315 / 2) Compatibility with multiplication / Existence of the multiplicative inverse / Associative, commutative and modulative properties

b = (2 / 9) · A - 35 Distributive property / Definition of multiplication / Result

The resulting expression for the base of the trapezoid is b = (2 / 9) · A - 35. (Correct choice: B)

To learn more on trapezoids: https://brainly.com/question/11908553

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