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stiv31 [10]
3 years ago
9

The length of a rectangle is three times it's width. If the width is diminished by 1 m and length is increased by 3 m, the area

of the rectangle that is formed is 72 m². Find the dimensions of the original rectangle.
Mathematics
1 answer:
Stella [2.4K]3 years ago
3 0

Answer: the length is 15 m and the width is 5 m

Step-by-step explanation:

Let L represent the original length of the rectangle.

Let W represent the original width of the rectangle.

The length of a rectangle is three times it's width. This means that

L = 3W

If the width is diminished by 1 m and length is increased by 3 m, the area of the rectangle that is formed is 72 m². This means that

(L + 3)(W - 1) = 72

LW - L + 3W - 3 - 72 = 72 + 3

LW - L + 3W = 75 - - - - -- - - - - - 1

Substituting L = 3W into equation 1, it becomes

3W × W - 3W + 3W = 75

3W² = 75

W² = 75/3 = 25

W = √25 = ±5

The width cannot be negative. Therefore, the width is 5 m

L = 3W = 3 × 5 = 15 m

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