Mathematics, 17.12.2019 23:31 Suphat

consider that the length of rectangle a is 21 cm and its width is 7 cm. which rectangle is similar to rectangle a?

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Answer from: 3peak101

Question is incomplete, complete question is given below.

Consider that the length of rectangle A is 21 cm and its width is 7 cm. Which rectangle is similar to rectangle A? A) A rectangle with a length of 9 cm and a width of 3 cm. B) A rectangle with a length of 20 cm and a width of 10 cm. C) A rectangle with a length of 18 cm and a width of 9 cm. D) A rectangle with a length of 27 cm and a width of 3 cm.

A) A rectangle with a length of 9 cm and a width of 3 cm.

Step-by-step explanation:

Given,

Length = 21 cm Width = 7 cm

$Ratio = \frac{Length}{Width}\\\\Ratio = \frac{21}{7}=3:1$

For the similarity of rectangle the ratio of length to width of any two rectangles should be equal.

So we have four options given;

A) A rectangle with a length of 9 cm and a width of 3 cm.

$Ratio =\frac{9}{3}=3:1$

Here the ratio is equal as of rectangle A. So this rectangle is similar to rectangle A.

B) A rectangle with a length of 20 cm and a width of 10 cm.

$Ratio =\frac{20}{10}=2:1$

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

C) A rectangle with a length of 18 cm and a width of 9 cm.

$Ratio =\frac{18}{9}=2:1$

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

D) A rectangle with a length of 27 cm and a width of 3 cm.

$Ratio =\frac{27}{3}=9:1$

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

Thus the correct option is A) A rectangle with a length of 9 cm and a width of 3 cm.

Answer from: Quest

step-by-step explanation: the answer for wha if rt is 10 centimeters long, and wha is st? it’s 6

Answer from: Quest

$2^{2x+11}=3^{x-31}$

take the logarithm of both sides (the base of the log doesn't matter):

$\ln2^{2x+11}=\ln3^{x-31}$

apply the exponent property - this says that $\ln a^b=b\ln a$ :

$(2x+11)\ln2=(x-31)\ln3$

distribute the log terms on both sides:

$(2\ln2)x+11\ln2=(\ln3)x-31\ln3$

group like terms together:

$(2\ln2-\ln3)x=-11\ln2-31\ln3$

divide through both sides by the coefficient on $x$ :

$x=-\dfrac{11\ln2+31\ln3}{2\ln2-\ln3}$

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

$x=-\dfrac{\ln2^{11}+\ln3^{31}}{\ln2^2-\ln3}$

$x=-\dfrac{\ln2^{11}3^{31}}{\ln\frac43}$

$x=-\log_{4/3}2^{11}3^{31}$

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