Question

Parallelogram KLMN is similar to parallelogram PQRS.

If the length of MN is 28 cm, the length of LM is 8 cm, and the length of QR is 4 cm, what is the length of RS?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length of RS, we need to use the property of similar figures.

Since parallelogram KLMN is similar to parallelogram PQRS, the corresponding sides are proportional.

This means that the ratio of the lengths between the two parallelograms is equal.

Therefore, we can set up the proportion as follows:

LM/MN = QR/RS

8/28 = 4/RS

Cross multiply to solve for RS:

8 * RS = 4 * 28

8RS = 112

RS = 112 / 8

RS = 14

Therefore, the length of RS is 14 cm.

Answer 2

Convert the following decimal into a rational number

0.1

Answer 3

[AI-generated answer — Bot GPT 3.5]

To convert the decimal 0.1 into a rational number, we need to represent it as a fraction.

In this case, 0.1 can be written as 1/10, since it is equivalent to one-tenth.

Therefore, the rational representation of 0.1 is 1/10.

Answer 4

Lars put stakes in his backyard, as shown in the diagram below, to separate sections of his garden.

Lars stretched 16 yards of a string from stake X to stake Y and 12 yards of the string from stake Y to stake Z. The two strings meet at a right angle.

He wants to stretch the string from stake Z to stake X next. What is the distance from stake Z to stake X?

Answer 5

[AI-generated answer — Bot GPT 3.5]

Since the two strings meet at a right angle, we can use the Pythagorean theorem to find the distance from stake Z to stake X.

Let's denote the distance from stake Z to stake X as d.

According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse. In this case:

(16)^2 + (12)^2 = d^2

Solving for d^2:

256 + 144 = d^2

400 = d^2

Taking the square root of both sides to find d:

d = √400

d = 20

Therefore, the distance from stake Z to stake X is 20 yards.