The length of a rectangular painting is 3 inches longer than its width. if the diagonal is 15 inches long, what is the length of the painting? a. 9 inches b. 12 inches c. 13 inches d. 18 inches

ANSWER

12 inches

EXPLANATION

Let the length of the rectangular painting be inches, then the width will be inches.

Since the diagonal is the hypotenuse, we can apply the Pythagoras Theorem to find the length.

We expand to obtain;

We simplify to obtain a quadratic equation in .

We divide through by 2 to obtain.

We factor to obtain

Since we are dealing with length we discard the negative value.

Hence the length is 12 inches

B. 12 inches

Step-by-step explanation:

We know that the length of the rectangular painting is 3 inches longer than its width so we can write it as:

l = w + 3

and the diagonal is 15 inches long.

We can use use the Pythagoras Theorem to find the length of the painting.

(w)² + (w + 3)² = (15)²

w² + w² + 6w + 9 = 225

2w² + 6w - 216 = 0

w² + 3w - 108 = 0

(w + 12)(w - 9) = 0

w = -12 (ignore), w = 9  

So, l = w + 3

l = 12

Therefore, the length of the rectangle is 12 inches.

step-by-step explanation: