Question

The Kahn's Family lives in a house that has a backyard in the shape of an isosceles trapezoid and a triangle. The area of the backyard can be expressed as the sum of the area of the triangle and the area of the trapezoid, which is 1/2bh+1/2(p+q)L The base and the height of the triangle are represented by b and h, respectively. The bases of the trapezoid are p and q, and the height of the trapezoid is L. 2 Rearrange the formula to find the length of base as a function of the lengths of the other sections of the backyard.

Answer 1

This is solved the way any 2-step linear equation is solved:

1. subtract the term not containing the variable of interest, then
2. divide by the coefficient of that variable.

... A = (1/2)bh + (1/2)(p+q)L

... A - (1/2)(p+q)L = (1/2)bh . . . . . subtract the term on the right

... (A -(1/2)(p+q)L)/(1/2·h) = b . . . .divide by (1/2)h, the coefficient of b

... b = (2A -(p+q)L)/h . . . . . . . . . . simplify