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3 years ago

Given that abcd ~Jklm. Find the value of x, y, and z

Mathematics

1 answer:

Minchanka [31]3 years ago

4 0

Answer:

x = 7.2

y = 10

z = 6

Step-by-step explanation:

Since ABCD ~ JKLM, therefore, the ratio of their corresponding sides would be equal. Thus:

JK/AB = KL/BC = LM/CD = JM/AD

Substitute

12/x = y/6 = 15/9 = 10/z

✔️Find x:

12/x = 15/9

12/x = 5/3

Cross multiply

x*5 = 3*12

5x = 36

x = 36/5

x = 7.2

✔️Find y:

y/6 = 15/9

y/6 = 5/3

Cross multiply

y*3 = 5*6

3y = 30

y = 30/3

y = 10

✔️Find z:

15/9 = 10/z

5/3 = 10/z

Cross multiply

5*z = 10*3

5z = 30

z = 30/5

z = 6

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Read 2 more answers

From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th

wel

Answer:

$\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}$

Step-by-step explanation:

The <u>width</u> of a square is its <u>side length</u>.

The <u>width</u> of a circle is its <u>diameter</u>.

Therefore, the largest possible circle that can be cut out from a square is a circle whose <u>diameter</u> is <u>equal in length</u> to the <u>side length</u> of the square.

<u>Formulas</u>

$\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}$

$\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}$

$\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}$

If the diameter is equal to the side length of the square, then:
$\implies \sf r=\dfrac{1}{2}s$

Therefore:

$\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}$