Question

Shreya has a photo that is 16 cm tall and 20 cm wide. She wants to put a frame around the photo which would have the same width all around.
Represent the area of the whole frame as a polynomial in terms of the width around the photo.
A.$x^{2} + 36x + 320$

B.$-4x^{2} - 72x + 320$

C.$4x^{2} + 72x + 320$

D.$-x^{2} - 36x - 320$

Answer 1

A photo is usually rectangular in shape. This means that if a frame is to be put around the photo with the same width all round, it means that if the width is "x", then the new length and width will be (l + 2x) and (w + 2x) respectively where l is length and w is width.

Option C is the correct answer

Data Given;

Height of Photo: 16 cm

Width of Photo: 20 cm

Since she wants to put a frame with same width around the photo, let's represent this width as x.

Thus;

New height = 16 + 2x

New width = 20 + 2x

Area of a rectangle is given as:

A = Length * width

Thus, in this case;

A = (16 + 2x) × (20 + 2x)

Multiplying out, we have;

A =  $4x^{2} + 32x + 40x + 320$

A = 4$x^{2} + 72x + 320$

Looking at the given options, Option C is the correct answer

Read more at: brainly.com/question/11289399