Question

The Saxena family plans to install a light to illuminate part of their rectangular yard. Nikki and Dylan each proposed a different spot to place the light. The proposed placements and the lit area that each produces are shown below.

Nikki's proposed placemat has a triangular light area with a base of 60 feet and height of 38 feet. Dylan's proposed placemat has a base of 60 feet and a height of 38 feet.

How do Nikki’s and Dylan’s proposals compare? Check all that apply.
Nikki’s proposed placement will light a greater area than Dylan’s placement.
Dylan’s proposed placement will light a greater area than Nikki’s placement.
Both proposed placements will light the same sized area.
Nikki’s proposed placement will light more than half the yard.
Dylan’s proposed placement will light more than half the yard.
Dylan’s proposed placement will light exactly half of the yard.
Nikki’s proposed placement will light less than half of the yard.

Answer 1

Nikki's and Dylan's proposed placements for the light will light the same sized area since both proposals have an identical triangular lit area with a base of 60 feet and a height of 38 feet, leading to an area of 1,140 square feet each.

Step-by-step explanation:

The question involves comparing the areas lit by two different placements of a light in the Saxena family's yard.

Both Nikki's and Dylan's proposed placements produce a triangular lit area with a base of 60 feet and a height of 38 feet.

To compare who's proposed placement will light a greater area, we need to calculate the area of a triangle using the formula Area = 1/2 × base × height.

Nikki's placement:

• Base = 60 feet
• Height = 38 feet
• Area = 1/2 × 60 × 38 = 1,140 square feet

Dylan's placement (identical dimensions):

• Base = 60 feet
• Height = 38 feet
• Area = 1,140 square feet

Since both placements produce the same area, we can conclude that:

• Both proposed placements will light the same sized area.