One side of a rectangle is 6 longer than the adjacent side. The area is 187. What are the dimensions?

2 Answers
May 2, 2018

17 and 11

Explanation:

The area of a rectangle is A=l*w. We can use variable x for l, and since we know the other side is 6 longer, we can use (x+6) for this side. And we know A=187. Inputting these values:
187=x(x+6) Distribute:
187=x^2+6x Set equal to 0:
x^2+6x-187=0 11,17 are factors of 187 and can be subtracted to 6, so we can factor the equation:
(x+17)(x-11)=0
17 and 11 work for the situation, so they are the dimensions.

May 2, 2018

The sides of the rectangle are 11 and 17.

Explanation:

let a,b be the sides of the rectangle with b being the loonger side
b=a+6
Thus a*b = area of rectangle
a(a+6) = 187
a^2+6a = 187
a^2+6a-187 = 0
a^2+17a-11a-187 = 0
a(a+17)-11(a+17) = 0
(a+17)(a-11) = 0
a=11 or -17
a=positve number
a=11
b=a+6
b=11+6=17

therefore the sides of the rectanlge are 11 and 17.