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

Explanation:

Step1: Find original area

The original length is 6 inches and width is 5 inches. The area of a rectangle is $A = lw$, so the original area $A_1=6\times5 = 30$ square - inches.

Step2: Find new - length and new - width

When each dimension is increased by $x$ inches, the new length is $(6 + x)$ inches and the new width is $(5 + x)$ inches.

Step3: Find new area

The new area $A_2=(6 + x)(5 + x)$ square - inches.

Step4: Use the area - relation

We know that the new area triples the original area. Since the original area is 30 square inches, the new area is $3\times30=90$ square inches. So the equation is $(x + 6)(x + 5)=90$.

Answer:

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