Question

Each rectangle has its area written inside and the expression mod

Answer 1

Answer:

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 = $\frac{18}{6}$ = 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 = $\frac{21}{7}$

⇒ x = 3

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