Question

Galina is finding the area of triangle RST. To do so, she follows the steps in the table.

Step 1 Draw a rectangle around triangle RST.

Step 2
Find the area of the rectangle.

Step 3 Find the area of the three right triangles created
by the sides of the rectangle and the intersection
with each vertex of the triangle.

Step 4
Subtract the area of the right triangles from
the area of the rectangle.

To solve the problem using these steps, what are the dimensions of the rectangle she should draw?

A. 2 units by 4 units
B. 3 units by 4 units
C. 3 units by 5 units
D. 4 units by 5 units (Dumb answers will be reported)

Answer 1

The answer is B

Explanation:

Answer 2

1 step: to draw a rectangle around triangle RST, you should

• draw points A(-1,-1), B(-1,3) and C(2,3);
• connect points A, B, C and T consecutively.

2 step: rectangle ABCT has length AB=4 units and width BC=3 units. Then

`A_(ABCT)=4\cdot 3=12` sq. un.

3 step:

`A_(\triangle ART)=(1)/(2)AR\cdot AT=(1)/(2)\cdot 2\cdot 3=3` sq. un.

`A_(\triangle BRS)=(1)/(2)BR\cdot BS=(1)/(2)\cdot 2\cdot 2=2` sq. un.

`A_(\triangle SCT)=(1)/(2)CS\cdot CT=(1)/(2)\cdot 1\cdot 4=2` sq. un.

4 step:

`A_(\triangle RST)=A_(ABCT)-A_(\triangle ART)-A_(\triangle BRS)-A_(\triangle SCT)=12-3-2-2=5` sq. un.

Answer: in step two you write dimensions of rectangle ABCT: length 4 units and width 3 units. Correct choice is B.