Question

1. a rectangle has a length of 8 cm and a width of 5 cm. if the dimensions are scaled by a factor of 3, what is the area of the new rectangle? a. 240 cm² b. 180 cm² c. 120 cm² d. 360 cm² 19. a triangle has a base of 6 cm and a height of 4 cm. if the scale factor is 1/2, what is the area of the scaled triangle? a. 6 cm² b. 12 cm² c. 24 cm² d. 3 cm²

Explanation:

Question 18

Step1: Find scaled length and width

Original length \( l = 8 \, \text{cm} \), scale factor \( k = 3 \), so scaled length \( l' = 8 \times 3 = 24 \, \text{cm} \).
Original width \( w = 5 \, \text{cm} \), scaled width \( w' = 5 \times 3 = 15 \, \text{cm} \).

Step2: Calculate area of new rectangle

Area of rectangle \( A = l' \times w' \), so \( A = 24 \times 15 = 360 \, \text{cm}^2 \)? Wait, no, wait—wait, 8×3=24, 5×3=15, 24×15=360? But wait, let's check again. Wait, 83=24, 53=15, 2415=360. But wait, the options have D as 360. Wait, but let me recheck. Wait, original area is 85=40. When scaling dimensions by 3, area scales by \( 3^2 = 9 \), so 40*9=360. Yes, that's correct.

Step1: Find scaled base and height

Original base \( b = 6 \, \text{cm} \), scale factor \( k = \frac{1}{2} \), so scaled base \( b' = 6 \times \frac{1}{2} = 3 \, \text{cm} \).
Original height \( h = 4 \, \text{cm} \), scaled height \( h' = 4 \times \frac{1}{2} = 2 \, \text{cm} \).

Step2: Calculate area of scaled triangle

Area of triangle \( A = \frac{1}{2} \times b' \times h' \), so \( A = \frac{1}{2} \times 3 \times 2 = 3 \, \text{cm}^2 \)? Wait, no—wait, original area is \( \frac{1}{2} \times 6 \times 4 = 12 \, \text{cm}^2 \). When scaling dimensions by \( \frac{1}{2} \), area scales by \( (\frac{1}{2})^2 = \frac{1}{4} \), so 12 * \( \frac{1}{4} = 3 \, \text{cm}^2 \). Yes, that's correct.

Answer:

D. \( 360 \, \text{cm}^2 \)

Question 19