The base of triangle T is 40 percent less than the length os rectangle R. The height T is 50 percent greater than the width of rectangle R. The area of triangle T is what percent of the area of rectangle R?

Options

A. `10`
B. `45`
C. `90`
D. `110`

Answer

To solve the problem, we need to find the area of triangle T as a percentage of the area of rectangle R. Let's break it down step by step.

### Step 1: Define Variables
Let the length of rectangle R be \( L \) and the width of rectangle R be \( W \).

### Step 2: Calculate the Base of Triangle T
The base of triangle T is 40% less than the length of rectangle R. Therefore, we can express the base \( B \) of triangle T as:
\[ B = L - 0.4L = 0.6L \]

### Step 3: Calculate the Height of Triangle T
The height of triangle T is 50% greater than the width of rectangle R. Thus, we can express the height \( H \) of triangle T as:
\[ H = W + 0.5W = 1.5W \]

### Step 4: Calculate the Area of Triangle T
The area \( A_T \) of triangle T can be calculated using the formula for the area of a triangle:
\[ A_T = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times B \times H \]
Substituting the values of \( B \) and \( H \):
\[ A_T = \frac{1}{2} \times (0.6L) \times (1.5W) = \frac{1}{2} \times 0.6 \times 1.5 \times L \times W \]
Calculating the constants:
\[ A_T = \frac{1}{2} \times 0.9 \times L \times W = 0.45LW \]

### Step 5: Calculate the Area of Rectangle R
The area \( A_R \) of rectangle R is given by:
\[ A_R = L \times W \]

### Step 6: Calculate the Percentage of the Area of Triangle T to Rectangle R
To find what percent the area of triangle T is of the area of rectangle R, we use the formula:
\[ \text{Percentage} = \left( \frac{A_T}{A_R} \right) \times 100 \]
Substituting the areas:
\[ \text{Percentage} = \left( \frac{0.45LW}{LW} \right) \times 100 = 0.45 \times 100 = 45\% \]

### Final Answer
The area of triangle T is 45% of the area of rectangle R.

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