the length of a rectangular frame is 5 cm more than the width. the area inside the frame is 66 square cm. find the width of the frame.
L = W + 5
A = L * W
( W + 5 ) * W = 66
W ^ 2 + 5 W = 66
W ^ 2 + 5 W - 66 = 0
Solutions of equation are :
W = - 11
and
W = 6
Length can't be negative so :
W = 6 cm
Proof:
L = W + 5 = 6 + 5 = 11
A = L * W = 11 * 6 = 66 cm ^ 2
To solve this problem, we will set up an equation based on the given information and solve for the width of the frame.
Let's assume the width of the frame is "W" cm.
According to the given information, the length of the frame is 5 cm more than the width, so the length can be expressed as "W + 5" cm.
The area inside the frame is given as 66 square cm, so we can set up the following equation:
(W + 5) * W = 66
Now, let's solve the equation to find the value of W.
Expanding the equation, we get:
W^2 + 5W = 66
Rearranging the equation to the standard quadratic form, we have:
W^2 + 5W - 66 = 0
Now, we can factor this quadratic equation:
(W + 11)(W - 6) = 0
Setting each factor equal to zero and solving for W, we have:
W + 11 = 0 --> W = -11 (discard this value since width cannot be negative)
W - 6 = 0 --> W = 6
Therefore, the width of the frame is 6 cm.