Exercise 49 Page 634

We are told that the area of the given trapezoid is 42m^2, while its height and one of the bases are 7 m and 4m respectively. We are asked to find the length of the other base, we can call it b_2. Let's begin by drawing a graph.

Recall that the area of a trapezoid is one half the product of its height and the sum of its bases. To find the length of the other base b_2, let's substitute the values A = 42m^2 , h=7m , and b_1 = 4 m into the formula for the area of a trapezoid.

A=1/2h(b_1+b_2)

SubstituteValues

Substitute values

42=1/2(7)(4+ b_2)

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Evaluate right-hand side

MoveRightFacToNumOne

1/b* a = a/b

42=7/2(4+b_2)

MultEqn

LHS * 2=RHS* 2

84=7(4+b_2)

DivEqn

.LHS /7.=.RHS /7.

12=4+b_2

SubEqn

LHS-4=RHS-4

8=b_2

RearrangeEqn

Rearrange equation

b_2=8

The length of the other base is 8 m.