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3 years ago

The perimeter of a rectangle is 24mm. The length is 4mm less than triple the width. What are the dimensions of the rectangle

Mathematics

1 answer:

Bess [88]3 years ago

4 0

<h3>The length is equal to 8.</h3><h3>The width is equal to 4.</h3>

2l + 2w = 24

l = 3w - 4

Because we have a value for l, we can plug it into the first equation to solve for the exact value of w.

2(3w - 4) + 2w = 24

Distributive property.

6w - 8 + 2w = 24

Combine like terms.

8w - 8 = 24

Add 8 to both sides.

8w = 32

Divide both sides by 8.

w = 4

Now that we have a value for w, we can plug it into the second equation to solve for the exact value of l.

l = 3(4) - 4

l = 12 - 4

l = 8

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Lily, Louis, and Ben went to an arcade and won tokens for prizes. Louis won 4.5 times as many tokens as Ben. Lily won 8 more tok

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The expression that describes the number of tickets won by Lily is:

a = 8 + 4.5c where "a" is the number of tokens won by Lily and "c" is the number of tokens won by Ben

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Given that Lily, Louis, and Ben went to an arcade and won tokens for prizes

Let "a" be the number of tokens won by Lily

Let "b" be the number of tokens won by Louis

Let "c" be the number of tokens won by Ben

Given that Louis won 4.5 times as many tokens as Ben

So we can frame a equation as:

number of tokens won by Louis = 4.5 times as many tokens as Ben

number of tokens won by Louis = 4.5 x number of tokens won by Ben

$b = 4.5 \times c$

b = 4.5c

Given that Lily won 8 more tokens than Louis

number of tokens won by Lily = 8 + number of tokens won by Louis

a = 8 + b

Substituting the value of b = 4.5c in above expression

a = 8 + 4.5c

Thus the expression that describes how many tokens Lily won is found

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