2 answers

A parallelogram has a base of length #2x+1#, a height of #x+3#, and an area of 42 square units. What

Question:

A parallelogram has a base of length #2x+1#, a height of #x+3#, and an area of 42 square units. What are the base and height of the parallelogram?

Answers

Base is 7, Height is 3.

Explanation:

The area of any parallelogram is Length x Width (Which is sometimes called height, depends on the textbook). We know that the length is #2x+1# and the Width (AKA Height) is #x+3# so we put them into an expression following Length x Width = Area and solve to get x=3. We then plug it into each equation to get 7 for the base and 6 for the height.

.

length = #2(3) + 1# = 7
height = #(3) + 3# = 6

Explanation:

#Area = base xx height#

#(2x+1)(x+3) = 42#

#2x^2 + 6x + x + 3 - 42 = 0# [make quadratic = 0]

#2x^2 + 7x - 39 = 0# [factorise]

#(2x +13)(x-3) = 0#

# x = -6 1/2# or #x =3#

Reject #-6 1/2# because a side cannot be negative.

#x = 3#

.

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