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

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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.

Approved by eNotes Editorial Team