Question

A rectangular playground has an area of 180 square yards. The length of the playground is 3 yards longer than the width. Find the length of the playground.
A)15 yards
B)18 yards
C)12 yards
D)13 yards

Answer 1

Answer:
A. 15 yards

Explanation hope it really help

Answer 2

Answer: The length is 15 yards so the answer is A.

Step-by-step explanation:

If  the length is 3 more than the width  the we will represent it by the equation L = w+3    where w is the width and to find the area of a rectangle, we need to multiply the length by the width. so the length is w+3 and the width is w so

w(w+3) = 180   solve for the w

w^2 + 3w = 180     subtract 180 from both sides

w^2 + 3w -180 = 0    find two numbers that their product is -180 and add to 3.

  the number 12 and -15 works out because -12*15= -180  and -15+ 12 =3

We will now have a new quadratic equation as

w^2 - 12w + 15w - 180 = 0  factor by grouping

w(w-12) 15(w-12)= 0     factor out w-12

(w-12)(w+15) = 0    set them both equal  zero.

w -12 = 0      or  w+15= 0  

w =  12      or  w = -15

Since we know that -15 can't represent a distance, then 12 is the width .  

So if we are to find the length and it gives us the information that the length is 3 yards more that the width then we will add 3 to the width to equal the length.

L= 12 +3

L = 15