The perimeter of a rectangular flower bed is 26 m .
If the length exceeds the breadth by 3 m , find its dimensions.
Lindiwe is twice as old as Preeya and six years older than Sue.
Their combined ages total 39 years.
How old is Lindiwe?

Question

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**Problem 1: Dimensions of the Rectangular Flower Bed**

Let the breadth be $$ b $$ and the length be $$ l $$. We are given:
- The perimeter $$ P = 26 $$ m.
- The length exceeds the breadth by 3 m, so $$ l = b + 3 $$.

The perimeter of a rectangle is given by:
$$
P = 2(l + b)
$$
Substitute the given values:
$$
2((b+3) + b) = 26
$$
Simplify:
$$
2(2b + 3) = 26
$$
Divide both sides by 2:
$$
2b + 3 = 13
$$
Subtract 3 from both sides:
$$
2b = 10
$$
Divide by 2:
$$
b = 5 \text{ m}
$$
Now, find the length:
$$
l = b + 3 = 5 + 3 = 8 \text{ m}
$$

---

**Problem 2: Ages of Lindiwe, Preeya, and Sue**

Let:
- $$ L $$ be Lindiwe's age,
- $$ P $$ be Preeya's age,
- $$ S $$ be Sue's age.

The conditions given are:
1. Lindiwe is twice as old as Preeya: 
   $$
   L = 2P
   $$
2. Lindiwe is six years older than Sue:
   $$
   L = S + 6 \quad \text{or} \quad S = L - 6
   $$
3. Their combined ages total 39 years:
   $$
   L + P + S = 39
   $$

Substitute $$ P = \frac{L}{2} $$ and $$ S = L - 6 $$ into the sum:
$$
L + \frac{L}{2} + (L - 6) = 39
$$
Combine like terms:
$$
L + \frac{L}{2} + L = \frac{2L}{2} + \frac{L}{2} + \frac{2L}{2} = \frac{5L}{2}
$$
Thus, the equation becomes:
$$
\frac{5L}{2} - 6 = 39
$$
Add 6 to both sides:
$$
\frac{5L}{2} = 45
$$
Multiply both sides by 2:
$$
5L = 90
$$
Divide by 5:
$$
L = 18
$$

**Final Answers:**

- The breadth of the flower bed is $$ 5 $$ m and the length is $$ 8 $$ m.
- Lindiwe is $$ 18 $$ years old.
- The flower bed is 5 meters in breadth and 8 meters in length. - Lindiwe is 18 years old.

The perimeter of a rectangular flower bed is 26 m .
If the length exceeds the breadth by 3 m , find its dimensions.
Lindiwe is twice as old as Preeya and six years older than Sue.
Their combined ages total 39 years.
How old is Lindiwe?

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The perimeter of a rectangular flower bed is 26 m . If the length exceeds the breadth by 3 m , find its dimensions. Lindiwe is twice as old as Preeya and six years older than Sue. Their combined ages total 39 years. How old is Lindiwe?

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Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions

The perimeter of a rectangular flower bed is 26 m .
If the length exceeds the breadth by 3 m , find its dimensions.
Lindiwe is twice as old as Preeya and six years older than Sue.
Their combined ages total 39 years.
How old is Lindiwe?