Answered

Join the growing community of curious minds on IDNLearn.com. Find the information you need quickly and easily with our reliable and thorough Q&A platform.

(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 greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.