Question

Kiana wants to cover and area of her backyard with concrete patio stones in the shape of a right triangle each stone cost 0.42$ and covers 29.26 squares inches .Each square grid represents 1 square foot if R(1,1) E(7,9) and D(I5,3) what is the minimum number of stones Kiana should by to cover a right triangular area in her backyard show work below.Steps:1 what is the length of ER round your answer to the nearest tenth2. What is the length of ED leave your answer to the nearest tenth 3 what is the area of the triangle 4 what is the minimum number of stones required 5 what will the cost to the nearest dollar

Answer 1

The length of a segment with endpoints in (x1, y1) and (x2, y2) is calculated as:

$\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

Then, the distance from E(7,9) to R(1,1) is:

$\sqrt[]{(1-7)^2+(1-9)^2}=\sqrt[]{(-6)^2+(-8)^2}=\sqrt[]{100}=10$

At the same way, the distance from E(7,9) to D(15,3) is:

$\sqrt[]{(15-7)^2+(3-9)^2}=\sqrt[]{8^2+(-6)^2}=\sqrt[]{100}=10$

Therefore ER has a length of 10 ft and ED has a length of 10 ft, So the area of the triangle is calculated as:

$\text{Area}=\frac{ER\cdot ED}{2}=\frac{10\cdot10}{2}=50ft^2$

Because ER and ED are the base and the height of the right triangle

Now, we need to transform 50 square feet into square inches as:

$50ft^2=50ft^2\cdot\frac{144in^2}{1ft^2}=7200in^2$

Now, the minimum number of stones required is calculated as:

$\frac{7200in^2}{29.26in^2}=246.069\approx247$

Because every stone cover 29.26 square inches

Finally, the total cost of the stones is:

247 * $0.42 = $103.74

Because every stone has a cost of $0.42

Answers: 1. 10 ft

2. 10 ft

3. 50 ft^2 = 7200 in^2

4. 247

5. $103.74