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1 year ago

Solve for x. The number that is cut off is 14. Suppose that both figures are similar.

Mathematics

1 answer:

Mekhanik [1.2K]1 year ago

5 0

Since both rectangles are similar, the following ratio must be fulfilled:

$\frac{x+9}{14}=\frac{9}{6}$

By multiplying both sides by 14, we get

$\begin{gathered} x+9=\frac{9\times14}{6} \\ x+9=21 \end{gathered}$

and by subtracting 9 to both sides, we have

$x=12$

Therefore, the answer is 12.

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Right triangles abc and dbc with right angle c are given below. If cos(a)=15,ab=12 and cd=2, find the length of bd.

dmitriy555 [2]

see the attached figure to better understand the problem

we have that

$cos(A)=\frac{1}{5} \\ AB=12\ units\\ CD=2\ units$

Step 1

Find the value of AC

we know that

in the right triangle ABC

$cos (A)=(AC/AB)\\AC=AB*cos(A)$

substitute the values in the formula

$AC=12*(1/5)\\ AC=2.4\ units$

Step 2

Find the value of BC

we know that

in the right triangle ABC

Applying the Pythagorean Theorem

$AB^{2} =AC^{2}+BC^{2}\\ BC^{2}=AB^{2} -AC^{2}$

substitute the values

$BC^{2}=12^{2} -2.4^{2}\\BC^{2}= 138.24\\ BC=11.76\ units$

Step 3

Find the value of BD

we know that

in the right triangle BCD

Applying the Pythagorean Theorem

$BD^{2} =DC^{2}+BC^{2}$

substitute the values

$BD^{2} =2^{2}+11.76^{2}$

$BD=11.93\ units$

therefore

the answer is

the length of BD is 11.93 units

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