QuestionXavier's papaya trees cover $370 \mathrm{~m}^{2}$ . The perimeter for pineapple trees is $84 \mathrm{~m}$ . Find their area.

Studdy Solution

STEP 1

Assumptions1. The land where the papaya trees are planted is a rectangle with an area of $370 \mathrm{~m}^{}$ . . The land where the pineapple trees are planted is also a rectangle with a perimeter of $84 \mathrm{~m}$ .
3. The two rectangles are identical in shape, meaning they have the same length and width.

STEP 2

Since the two rectangles are identical, we can use the properties of the rectangle to find the length and width. The area of a rectangle is given by the formula $Area = Length \\times Width$

STEP 3

We can rearrange the formula to find the width of the rectangle where the papaya trees are planted.
$Width = Area / Length$

STEP 4

However, we don't have the length yet. But we know that the perimeter of a rectangle is given by the formula $Perimeter =2 \\times (Length + Width)$

STEP 5

We can rearrange this formula to find the length of the rectangle where the pineapple trees are planted.
$Length = (Perimeter /2) - Width$

STEP 6

We can now substitute the formula for width from step3 into the formula for length from step5.
$Length = (Perimeter /2) - (Area / Length)$

STEP 7

This is a quadratic equation in terms of length. We can solve this equation to find the length.

STEP 8

First, we multiply through by length to clear the fraction.
$Length^2 = (Perimeter /2) \\times Length - Area$

STEP 9

Rearrange the equation to the standard form of a quadratic equation.
$Length^2 - (Perimeter /2) \\times Length + Area =$

STEP 10

Now, plug in the given values for the perimeter and area to solve the quadratic equation.
$Length^2 - (84 /2) \\times Length +370 =0$

STEP 11

olve the quadratic equation to find the length. Remember that a quadratic equation has two solutions, but in this case, we are only interested in the positive solution because length cannot be negative.

STEP 12

Once we have the length, we can substitute it back into the formula for width from step to find the width.

STEP 13

Finally, we can find the area of the land where the pineapple trees are planted by substituting the length and width into the formula for area from step2.
$Area = Length \\times Width$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms