Answer :
Let's tackle each part of the question step by step.
(p) Finding the value of [tex]x[/tex]:
Given:
- Length of the rectangle = [tex]x + 3[/tex] metres
- Breadth of the rectangle = [tex]x - 2[/tex] metres
- Perimeter of the rectangle = 38 metres
We know that the formula for the perimeter [tex]P[/tex] of a rectangle is:
[tex]P = 2 \times (\text{Length} + \text{Breadth})[/tex]
Substitute the given values into the formula:
[tex]38 = 2 \times ((x + 3) + (x - 2))[/tex]
Simplify the expression inside the parentheses:
[tex]38 = 2 \times (2x + 1)[/tex]
Now distribute the 2 to terms inside the parentheses:
[tex]38 = 4x + 2[/tex]
Subtract 2 from both sides to isolate terms with [tex]x[/tex]:
[tex]36 = 4x[/tex]
Divide by 4 to solve for [tex]x[/tex]:
[tex]x = 9[/tex]
(q) Finding the length when breadth and area are given:
Given:
- Breadth of the rectangle = 12 metres
- Area of the rectangle = 180 m²
We know that the formula for the area [tex]A[/tex] of a rectangle is:
[tex]A = \text{Length} \times \text{Breadth}[/tex]
Substitute the given values into the formula:
[tex]180 = \text{Length} \times 12[/tex]
Solve for Length:
Divide both sides by 12:
[tex]\text{Length} = \frac{180}{12} = 15 \, \text{metres}[/tex]
Therefore, the value of [tex]x[/tex] is 9, and the length of the rectangle when its breadth is 12 metres and the area is 180 m² is 15 metres.
