Pilar is a landscaper and is working on the design of a square garden. She wants to divide it into two triangles, in one she wants to plant grass and in the other she will put a wooden terrace. The information she has is that the diagonal measures v80 m, the cost of grass is $4,500 per square meter and the cost of wood is $6,500 per square meter. How much would you spend on the garden?

To calculate the cost of the garden, we first need to find the area of the square garden and then determine the cost of grass and wood for the two triangular sections. Given: The diagonal measures √80 meters. Let's find the length of one side of the square garden using the diagonal: Let "s" be the length of one side of the square. We know that the diagonal divides the square into two right-angled triangles. By the Pythagorean theorem, we have: � 2 + � 2 = ( 80 ) 2 s 2 +s 2 =( 80 ​ ) 2 Simplify: 2 � 2 = 80 2s 2 =80 Divide by 2: � 2 = 40 s 2 =40 Take the square root: � = 40 = 2 10 s= 40 ​ =2 10 ​ meters Now, we can find the area of the square: Area of square = � 2 = ( 2 10 ) 2 = 4 × 10 = 40 s 2 =(2 10 ​ ) 2 =4×10=40 square meters Now, let's calculate the cost of grass and wood for the two triangular sections: Grass section: Area of one triangle = (1/2) * (base) * (height) The base and height of the triangle are equal to one side of the square, which is 2 10 2 10 ​ meters. Area of one grass triangle = (1/2) * 2 10 2 10 ​ * 2 10 2 10 ​ = 20 square meters Cost of grass for one triangle = 20 20 square meters * $4,500 per square meter = $90,000 Since there are two grass triangles, the total cost for grass = 2 * $90,000 = $180,000 Wood section (terrace): The area of the wooden terrace is the remaining area of the square after subtracting the grass area. Wood section area = Total square area - Grass area Wood section area = 40 40 square meters - 2 × 20 2×20 square meters = 40 40 square meters - 40 40 square meters = 0 0 square meters Cost of wood for the terrace = 0 0 square meters * $6,500 per square meter = $0 Now, let's calculate the total cost of the garden: Total cost = Cost of grass + Cost of wood Total cost = $180,000 + $0 = $180,000 Pilar would spend $180,000 on the garden.