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.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

The area of a triangle = (base x height) / 2

and,

both lights illuminate the same base and height = (60 x 38) / 2

= 1,140 sq ft

Both Dylan's and Nikki's proposed placement will lit exactly half of the yard.

The yard's total area = 60 x 38 = 2,280 sq ft,

which is twice the area lit by the lights.

Thus, The correct situation for the given condition are as follows:

C) Both proposed placements will light the same sized area.

F) Dylan's proposed placement will light exactly half of the yard.

Learn more about Area of triangle from:

https://brainly.com/question/27683633

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