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3 years ago

In a certain isosceles triangle, the base is 1 1/2 times as long as each leg and the perimeter is 63. How long is the base?

Mathematics

1 answer:

son4ous [18]3 years ago

6 0

Answer:

The base is 27 units long.

Step-by-step explanation:

This is a solve the system question. Call the length of the base B and the length of each leg L. We are told:

$B=1.5L$

and

$B+2L=63$

Sub the first equation into the second:

$1.5L+2L=63\\3.5L=63\\L=18$

Now that we have the leg length, sub that into either of the original equations to find the base. I'll use the first equation:

$B=1.5(18)\\B=27$

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Given:

$\overline{AB}\cong \overline {CD},\overline{BC}\cong \overline {DA}$

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Step-by-step explanation:

If there is a relationship of direct proportionality for every ordered pair of the table, then the constant of proportionality must the same for every ordered pair. The constant of proportionality ( $k$ ) is described by the following expression:

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Where:

$x$ - Input.

$y$ - Output.

If we know that $(x_{1}, y_{1}) = (13, 45.5)$ , $(x_{2}, y_{2}) = (14, 49)$ and $(x_{3}, y_{3}) = (15, 52.5)$ , then the constants of proportionalities of each ordered pair are, respectively: