Answered

Join the IDNLearn.com community and start finding the answers you need today. Join our community to access reliable and comprehensive responses to your questions from experienced professionals.

(a) Simplify.

(b) A wire of length 38 cm is bent into the shape of a rectangle whose length is 7 cm more than the width. Find the area of the rectangle.

(c) If a rope is 720 meters long, find half of the length of the rope.

Sagot :

GinnyAnsweridn
### Part (a): Simplification

Let's simplify the problem given in part (b) step by step.

### Part (b): Solving the Problem

#### Step 1: Understanding the Problem
We are given a wire of length 38 cm that is bent into the shape of a rectangle. The length of the rectangle is 7 cm more than the width. We need to find:
1. The width and length of the rectangle.
2. The area of the rectangle.
3. Given farone is 720 metres, find half of the length of the rope.

#### Step 2: Representing the Variables
Let's denote:
- The width of the rectangle by [tex]\( w \)[/tex] cm.
- The length of the rectangle by [tex]\( l \)[/tex] cm.

According to the problem, the length [tex]\( l \)[/tex] is 7 cm more than the width [tex]\( w \)[/tex]:
[tex]\[ l = w + 7 \][/tex]

#### Step 3: Using Perimeter to Formulate Equations
The perimeter [tex]\( P \)[/tex] of a rectangle is given by:
[tex]\[ P = 2 \times (l + w) \][/tex]

Given that the wire length (which is the perimeter) is 38 cm, we can write:
[tex]\[ 2 \times (l + w) = 38 \][/tex]

Substitute [tex]\( l = w + 7 \)[/tex] into the perimeter equation:
[tex]\[ 2 \times ((w + 7) + w) = 38 \][/tex]

Simplify and solve for [tex]\( w \)[/tex]:
[tex]\[ 2 \times (2w + 7) = 38 \][/tex]
[tex]\[ 4w + 14 = 38 \][/tex]
[tex]\[ 4w = 24 \][/tex]
[tex]\[ w = 6 \][/tex]

Thus, the width of the rectangle is [tex]\( w = 6 \)[/tex] cm.

#### Step 4: Calculate the Length
Using [tex]\( w = 6 \)[/tex] cm, we find the length [tex]\( l \)[/tex]:
[tex]\[ l = w + 7 \][/tex]
[tex]\[ l = 6 + 7 \][/tex]
[tex]\[ l = 13 \][/tex] cm

#### Step 5: Calculate the Area
The area [tex]\( A \)[/tex] of the rectangle is given by:
[tex]\[ A = l \times w \][/tex]
[tex]\[ A = 13 \times 6 \][/tex]
[tex]\[ A = 78 \][/tex] square cm

#### Step 6: Find Half of the Length of the Rope
Given farone is 720 metres, we need to find half of the length of the rope:
[tex]\[ \text{Half of 720 metres} = \frac{720}{2} = 360 \][/tex] metres

### Summary

1. The width of the rectangle is [tex]\( 6 \)[/tex] cm.
2. The length of the rectangle is [tex]\( 13 \)[/tex] cm.
3. The area of the rectangle is [tex]\( 78 \)[/tex] square cm.
4. Half of the length of the rope (farone) is [tex]\( 360 \)[/tex] metres.
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.