Question

The length of a rectangle is 6 inches, and the width is 5 inches. When each dimension is increased by x inches, the area triples. Which equation models this situation? A) (6x)(5x) = 60 B) (6x)(5x) = 90 C) (x + 6)(x + 5) = 60 D) (x + 6)(x + 5) = 90

Answer 1

D) (x + 6)(x + 5) = 90

Answer 2

Option D is correct.i.e., ( x + 6 ) × ( x + 5 ) = 90

Explanation:

Given: Length of Rectangle = 6 inches and Width of Rectangle = 5 inches

To find: Equation which represent the situation when length & width i increased by x inches and area becomes triple.

Area of Rectangle = Length × Width

= 6 × 5

= 30 inche²

Area of Rectangle, A = 30 inche²

When length and width are increased by x inches, new dimensions become

New Length = 6 + x = ( x + 6 ) inches

New Width = 5 + x = ( x + 5 ) inches

Area of new Rectangle = 3 × A = 3 × 30 = 90 inches²

As we know,

Area of New Rectangle = New Length × New Width

90 = ( x + 6 ) × ( x + 5 )

Therefore, Option D is correct.i.e., ( x + 6 ) × ( x + 5 ) = 90