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If a rectangle is 4 inches wide and 7 inches long. When the length and width are increased by the same amount, the area is increased by 26 square inches. What are the new dimensions.

1 Answer

4 votes

Answer:

New length =
2+7=9 inches

New width =
2+4=6 inches

Explanation:

Given:

Length of rectangle is 7 inches

Width of a rectangle is 4 inches

The area is increased by 26 square inches when the length and width are increased by the same amount.

To find: new length and width

Solution:

With length of rectangle is 7 inches and width of a rectangle is 4 inches,

area = 7Ă—4 = 28 inches

Let length and width be increased by x inches

New length = x + 7 inches

New Width = x + 4 inches

New area =
(x+7)(x+4)=x^2 +11x+28

Also, new area = 28 + 26 = 54 square inches.

So,


28+11x+x^2 =54\\x^2+11x-26=0\\x^2 +13x-2x-26=0\\x(x+13)-2(x+13)=0\\(x-2)(x+13)=0\\x= 2, -13

As dimension can not be negative,
x=-13 is rejected.

So,
x=2

New length =
2+7=9 inches

New width =
2+4=6 inches

User Erik Shilts
by
7.3k points
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