Question

The length of a rectangle is 5 meters longer than the width. If the area is 34 square meters, find the rectangle's dimensions. Round to the nearest tenth of a meter.

Answer 1

The dimensions of a rectangle with an area of 34 square meters and a length that is 5 meters longer than its width are approximately 4.4 meters for the width and 9.4 meters for the length, both rounded to the nearest tenth.

Step-by-step explanation:

The student has asked to find the dimensions of a rectangle given that the length is 5 meters longer than the width and the area is 34 square meters. To solve this, we can let the width be represented by 'w' and then the length will be 'w + 5'. The area of a rectangle is given by the formula Length × Width, so we have:

(w + 5) × w = 34

This is a quadratic equation. To solve for 'w', we first expand the equation to get:

w² + 5w - 34 = 0

Then, we find the roots using factorization or the quadratic formula. Upon solving, we find that the width 'w' is approximately 4.4 meters (rounding to the nearest tenth). The length will be 5 meters longer, which is approximately 9.4 meters. Thus, the rectangle's dimensions are approximately 4.4 meters for the width and 9.4 meters for the length, both rounded to the nearest tenth.

Answer 2

8.8 meter and 3.8 meter

Step-by-step explanation:

GIVEN: The length of a rectangle is
`5` meters longer than the width. If the area is
`34` square meters.

TO FIND: The rectangle's dimensions.

SOLUTION:

Let the length of the rectangle be
`l` and breadth be
`b`

According to question

`l=5+b`

Area of rectangle
`=\text{length}*\text{breadth}`

putting values,

`=l* b=(b+5)b=34`

`\implies b^2+5b=34`

`\implies b^2+5b-34=0`

on solving we get

`b=3.8\text{ meter}`

Similarly,
`l=8.8\text{ meter}`

Hence the length and breadth of rectangle are 8.8 meter and 3.8 meter respectively.