What multiplication problem is represented by the model?

Which set of numbers could represent the lengths of the sides of a right triangle?

DiKsa [7]

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

By the pythagorean theorem, a triangle is a right triangle if and only if

$\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2$ .

In this case,

$\text{longest side}^2 = 17^2 = 289$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}$ .

In other words, indeed $\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2$ . Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

Factor out the common factor $2$ to simplify the calculations.

$\text{longest side}^2 = 20^2 = 400$

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = 11^2 = 121$ .

<h3> $\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}$ .</h3>

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

6 0

3 years ago

Brendan is 30. Anna is 5 years older than Cassie and 10 years younger than Brendan. How old is Cassie

Keith_Richards [23]

Answer:

20 because Brendan is 30

6 0

2 years ago

Find Malcolm’s debt-to-income ratio if his monthly expenses are $975 and his monthly salary is $1200.

hjlf

Answer: D. 0.8125

Step-by-step explanation: His expenses is $975, and his salary is $1200. Divide the expenses by the salary to find the debt-to-income ratio.

975/1200 = 0.8125

The debt-to-income ratio is 0.8125.

7 0

3 years ago

Read 2 more answers

What is the approximate volume of the cylinder? Use 3.14 for π. high 8 length 6

Illusion [34]

Answer:

I got 226.08

Step-by-step explanation:

I don't know if your trying to find the nearest whole number

4 0

2 years ago

The width of a box is two inches less than twice the height. The length is 4 inches less than three times the height. The volume

Mrac [35]

Answer:

Dimensions are 8 Inches by 14 inches by 20 inches

Step-by-step explanation:

The volume of the box is 2240. This means:

lbh = 2240

Where b is the width.

Width is two inches less than twice the height

b = 2h - 2

length is 4 inches less than 3 times the height

l = 3h - 4

Substituting these parameters into the lbh equation will yield the following:

h * (3h - 4) * (2h - 2) = 2240

h[6h^2-14h+8] = 2240

6h^3 -14h^2 + 8h - 2240= 0

Solving this cubic equation will yield one of the values to be 8. The other two values are complex numbers.

b = 2h - 2

l = 3h - 4

b = 2(8) - 2 = 14

l = 3(8) - 4 = 20

6 0

3 years ago