The perimeter of a rectangle is 148mm. The height is fourteen more than three times the base. What is the area?

Expert Answers

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The perimeter is two times the base plus two times the height and equals 148.

2H+2B=148

The height is 14 more than three times the base.

H=14+3B

Write as a system of two equations with two unknowns.

H+B=74   (1)

H-3B=14  (2)

Multiply (1) by -1 and add to (2) to solve by elimination.

`-H-B=-74`

`H-3B=14`

----------------------

        `-4B=-60`

`B=15`

Substitute 15 for B in (1) and solve for H.

`H=74-15=59`

To verify substitute 59 for H and 15 for B in (2).

59-(3)(15)=14

59-45=14

Calculate the area of the rectangle.

`Area=BxH`

Substitute 15 for B and 59 for H.

`Area=15x59=885`

Thus the area of the rectangle is 885 mm.

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