Question

A rectangular painting has an area of 105 square inches. The length is 16 inches longer than the width
What is the length, in inches, of the painting?

Answer 1

Answer:

21

Step-by-step explanation:

I wil call the length l and the width w in the following. We are given these informations:

The area of the rectangle is 105. That means l * w = 105. (1)

The length is 16 inches longer that the width. That means l = w + 16. (2)

If we plug the information we get from (2) into the equation (1), we get:

(w + 16) * w = 105

Simplify and you get

w² + 16 w - 105 = 0

With the the quadratic formula we get the results w = 5 and w = -21. The negative result doesn't make sense for our task, we are only interested in positive length and width :).

If we now plug w = 5 back into our infromation (2), we get:

l = 5 + 16 = 21

(To confirm the result plug w = 5 and l = 21 into (1))

Answer 2

Length of rectangular painting is 21 inches

Area based problem:

Given that;

Area of rectangular painting = 105 square inches

Length of rectangular painting = 16 + Width of rectangular painting

Find:

Length of rectangular painting

Computation:

Assume;

Width of rectangular painting = a

Length of rectangular painting = 16 + a

So.

105 = (a)(a + 16)

a² + 16a - 105 = 0

a² + 21a - 5a - 105 = 0

a(a + 21) - 5(a + 21) = 0

(a + 21)(a - 5)

So,

Width of rectangular painting = 5 inches

Length of rectangular painting = 16 + 5

Length of rectangular painting = 21 inches

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