A rectangle has 30 cm as its length and 720 sq cm as its area. Its area is increased to 1 1/4 times its original area 4 by increasing only its length. Its new perimeter is

Options

A. a. 123 cm
B. b. 125 cm
C. c. 119 cm
D. d. 121 cm

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
We know the following:
- Length of the rectangle (L) = 30 cm
- Area of the rectangle (A) = 720 sq cm

### Step 2: Calculate the width of the rectangle
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
We can rearrange this to find the width (W):
\[ W = \frac{A}{L} \]
Substituting the known values:
\[ W = \frac{720 \text{ sq cm}}{30 \text{ cm}} = 24 \text{ cm} \]

### Step 3: Calculate the new area after increasing it to 1 1/4 times the original area
1 1/4 times the original area can be expressed as:
\[ \text{New Area} = \frac{5}{4} \times 720 \text{ sq cm} \]
Calculating this gives:
\[ \text{New Area} = 900 \text{ sq cm} \]

### Step 4: Set up the equation for the new length
Let the new length be \( L' \). Since the width remains unchanged, we can use the area formula again:
\[ \text{New Area} = L' \times W \]
Substituting the values we have:
\[ 900 \text{ sq cm} = L' \times 24 \text{ cm} \]
Now, solve for \( L' \):
\[ L' = \frac{900 \text{ sq cm}}{24 \text{ cm}} = 37.5 \text{ cm} \]

### Step 5: Calculate the new perimeter
The perimeter (P) of a rectangle is given by the formula:
\[ P = 2 \times (L + W) \]
Substituting the new length and the original width:
\[ P = 2 \times (37.5 \text{ cm} + 24 \text{ cm}) \]
Calculating this gives:
\[ P = 2 \times 61.5 \text{ cm} = 123 \text{ cm} \]

### Final Answer
The new perimeter of the rectangle is **123 cm**.

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