Mathematics: The perimeter of a triangle is 510 ft and the sides are in the ratio of 11: 16: 24. find the area of the triangle. need , is there a specific formula for this?

The perimeter of a triangle is 510 ft and the

Ответ:

sullydai6510

17.01.2022

1.
The side lengths are in the ratio 11:16:24, so let them be

11k, 16k, and 24k for some number k.

11k+16k+24k=510
k(11+16+24)=510
51k=510
k=10

so the actual sides are 110, 160 and 240 feet.

2.
There is a famous formula, called Heron's formula, which calculates the area of a triangle, given its sides a, b and c.

we first calculate the half perimeter, which we usually denote by u:

$u= \frac{a+b+c}{2}$

then the theorem states that the area A is as follows:

$A= \sqrt{u(u-a)(u-b)(u-c)}$

3.

In our case:

$u= \frac{a+b+c}{2} =\frac{110+160+240}{2} = \frac{510}{2}$

$u-a= \frac{510}{2} -110= \frac{510-220}{2} = \frac{290}{2}$

$u-b= \frac{510}{2} -160= \frac{510-320}{2} = \frac{190}{2}$

$u-a= \frac{510}{2} -240= \frac{510-480}{2} = \frac{30}{2}$

$A= \sqrt{\frac{510}{2}*\frac{290}{2}* \frac{190}{2} * \frac{30}{2}} =7,258.745$ feet squared

D 7,258.745 ft squared

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Ответ:

fia31

25.06.2020

Mathematics

67 degrees

Step-by-step explanation:

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The perimeter of a triangle is 510 ft and the sides are in the ratio of 11: 16: 24. find the area of the triangle. need , is there a specific formula for this?

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