Each rectangle has its area written inside and the expression mod

represents the area is written below the box. Find the side leng

rectangle.

ox. Find the side length of each

289 in?

1,225 in?

289 in?

36x2 – 12x + 1

25x2 - 50x + 25

49x2 – 56x + 16

Length of the boxes are 17 in, 35 in, 17 in.

Step-by-step explanation:

The given question is incomplete: please find the complete question in the attachment.

A). From Box - (1)

Area of the box = 289 in.²

Expression that denotes the area of the box = 36x² - 12x + 1

So, 36x²- 12x + 1 = 289

(6x)² - 2(6)x + (1)² = (17)²

(6x - 1)² = (17)² [ Since (a² - 2ab + b²) = (a - b)²]

Given box is a square having sides = (6x - 1) in.

∵ (6x - 1)² = 17

⇒ 6x = 18

⇒ x = = 3

Now length of the sides = (6x - 1) = 17 in.

B) Box - (2)

Similarly, 25x²- 50x + 25 = 1225

(25x² - 50x + 25) = (35)²

(5x - 5)² = (35)²

5(x - 1) = 35 ⇒ x = 8

Here length of one side of the box is 5(x - 1) = 5(8 - 1) = 35in.

C). Box - (3)

49x² - 56x + 16 = 289

(7x)² - 2×(7x)(4) + 4²= (17)²

(7x - 4)² = (17)²

Length of each side = (7x - 4) in.

From, (7x - 4)² = (17)²

7x - 4 = 17

⇒ x =

⇒ x = 3

Therefore, length of each side of the box = (7x - 4) = 17 in.

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

step-by-step explanation: