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Paraphin [41]
3 years ago
12

For a rectangular prism, if the base length was shrunk by a factor of two-thirds, the width was quadrupled, and height was cut i

n half, how would the changes affect the surface area formula? The attachment has the problem and the answer choices. Thanks.

Mathematics
1 answer:
Luden [163]3 years ago
5 0
Surface area = 2(wl + hl + hw) = 2wl + 2hl + 2hw

Conditions:
base length is shrunk by a factor of 2/3
width is quadrupled
height is cut in half.

l ⇒ 2l/3 w ⇒ 4w ; h ⇒ h/2

SA = <span>2wl + 2hl + 2hw
</span>SA = 2(4w)(2l/3) + 2(h/2)(2l/3) + 2(h/2)(4w)
SA = (16wl/3) + 4hl/6 + 8hw/2

Simplify:

SA = 16/3 wl + 2/3 hl + 4hw   Choice C.


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If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2
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If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width

Solution:

Let the length of rectangle=x

Width of rectangle=x/10

Perimeter is 2(Length+Width)

= 2(x+x/10)

Area of Rectangle= Length* Width=x*x/10

As, Perimeter=2(Area)

So,2(x+x/10)=2(x*x/10)

Multiplying the equation with 10, we get,

2(10x+x)=2x²

Adding Like terms, 10x+x=11x

2(11x)=2x^2

22x=2x²

2x²-22x=0

2x(x-11)=0

By Zero Product property, either x=0

or, x-11=0

or, x=11

So, Width=x/10=11/10=1.1

Checking:

So, Perimeter=2(Length +Width)=2(11+1.1)=2*(12.1)=24.2

Area=Length*Width=11*1.1=12.1

Hence, Perimeter= 2 Area

As,24.2=2*12.1=24.2

So, Perimeter=2 Area

So, Answer:Length of Rectangle=11 units

Width of Rectangle=1.1 units

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