Question

PLEASE HELP QUICKLY ​

Answer 1

1) x = 8 cm

2) x = 7m

3) x = 14 m

4) x = 1.875 in

Explanation:

In order to find the value of x, we can use the Total surface area of the cuboid formula:

`\boxed{\boxed{ \sf TSA = 2(lw + wh + hl) }}`

where

TSA = Total surface area

l = length of the cuboid

w = width of the cuboid

h = height of the cuboid

1)

Let's determine the value of x in the cuboid.

We are given that the surface area of the cuboid is 152 cm², the width is 2 cm, and the height is 6 cm. We need to find the length, which is represented by x.

We can set up an equation to represent the surface area of the cuboid:

2(wh + lh + wl)= 152

2wh + 2lh + 2wl = 152

Substituting the given values, we get:

2(2)(6) + 2(6)(x) + 2(2)(x) = 152

24 + 12x + 4x = 152

Combining like terms, we get:

16x +24 = 152

Subtracting 24 on both sides:

16x +24 = 152 - 24

16x = 128

Dividing both sides by 16, we get:

`\sf (16x )/(16) = (128)/(16)`

x = 8 cm

Therefore, the length of the cuboid is 8 cm.

2)

To find the value of x, we need to use the formula for the surface area of a cuboid. This formula is:

2(lw + wh + hl) = 166

We are given that the width (w) is 4 m, the height (h) is x m, and the length (l) is 5 m. We are also given that the surface area (S) is 166 m².

Substituting the given values into the formula, we get:

2(4x + 5x + 20) = 166

Combining like terms, we get:

2(9x + 20) = 166

18x + 40 = 166

Subtract both sides by 40.

18x + 40 - 40= 166 - 40

18x = 126

Dividing both sides by 18, we get:

`\sf (18x )/(18)= (126)/(18)`

x = 7

Therefore, the value of x is 7 m.

3)

To determine the value of x in the cuboid, we can use the formula for the surface area of a cuboid:

2(lw + wh + hl) = 292

We are given that the width (w) is 4 m, the height (h) is 5 m, and the length (l) is x m. We are also given that the surface area (S) is 292 m².

Substituting the given values into the formula, we get:

2(4x + 5x + 20) = 292

Combining like terms, we get:

2(9x + 20) = 292

18x + 40 = 292

Subtract 40 on both sides:

18x + 40 - 40 = 292 - 40

18x = 252

Dividing both sides by 18, we get:

`\sf (18x)/(18) = (252)/(18)`

x = 14

Therefore, the value of x is 14 m.

4)

Given the surface area of 31.25 in², width of 2.5 in², height of x , and length represented by 2.5in, we can use the formula for the surface area of a cuboid to find the value of x.

Substituting the given values into the formula, we get:

2(2.5x + 2.5x + 2.5(2.5)) = 31.25

Combining like terms, we get:

2(5x + 6.25) = 31.25

10x + 12.5 = 31.25

Subtracting 12.5 from both sides, we get:

10x + 12.5 - 12.5 = 31.25 - 12.5

10x = 18.75

Dividing both sides by 10, we get:

`\sf (10x)/(10) = (18.75)/(10)`

x = 1.875 in

Therefore, the value of x is 1.875 in.