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3 years ago

The perimeter of a rectangle is 108cm. The ration of its length to its width is 7:2 what is the area of the rectangle in cm2?

Mathematics

1 answer:

Mice21 [21]3 years ago

5 0

Answer:

504 cm²

Step-by-step explanation:

Let the length and the width of the rectangle be L cm and W cm respectively.

Perimeter= 2(L +W)

2(L +W)= 108

L +W= 108 ÷2

L +W= 54

L= 54 -W -----(1)

$\frac{L}{W} = \frac{7}{2}$

<em>Cross multiply:</em>

2L= 7W -----(2)

Substitute (1) into (2):

2(54 -W)= 7W

<em>Expand:</em>

108 -2W= 7W

<em>+2W on both sides:</em>

9W= 108

<em>Divide both sides by 9:</em>

W= 108 ÷9

W= 12

<em>Substitute W= 12 into (1):</em>

L= 54 -12

L= 42

Area of rectangle

= length ×width

= LW

= 42(12)

= 504 cm²

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2 years ago

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<h3>How to solve an algebraic expression?</h3>

Solving an expression algebraically involves basic operations like addition, subtraction, multiplication, and division.

In the expression, add/subtract the constant terms on both sides
Multiply/divide the coefficient of the variable on both sides
Solve for the variable.

<h3>Calculation:</h3>

Given that,

A tour company charges a given price per ticket based on the number 'n' of people who take the tour.

The maximum number of people who are allowed to take the tour is 35. I.e., n ≤ 35.

The price per ticket is $20 for n < 10 people and the price per ticket is given by the expression 20-(n-10)/2 for n > 10 people.

Harper goes on a tour where the ticket price is $10.50.

Since the price is less than $20, so the number of people who went on this tour is known by the expression 20-(n-10)/2 for n > 10 people.

So, solving the given expression:

20-(n-10)/2 = $10.50

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(n-10) = 9.5 × 2

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∴ n = 19 + 10 = 29

Therefore, 29 people went on this tour for a ticket price of $10.50.

Learn more about solving an expression here:

brainly.com/question/723406

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