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3 years ago

How could you find the perimeter of an isosceles right triangle if you (8) already know the area?

Mathematics

1 answer:

netineya [11]3 years ago

7 0

The area of a triangle is given in terms of the side lengths (b, h) as

... A = (1/2)bh

If b=h, then we can find the side length as ...

... A = (1/2)b²

... b = √(2A) . . . . . multiply by 2 and take the square root

The hypotenuse (x) can be found from the Pythagorean theorem:

... x² = b² + h² = 2b²

... x = b√2

The perimeter is the sum of the side lengths, so is

... P = b + b + x = 2√(2A) + (√(2A))·√2

... P = (2+√2)·√(2A)

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3 years ago

Read 2 more answers

Mileage tests are conducted for a particular model of automobile. If a 98% confidence interval with a margin of error of 1 mile

Llana [10]

Answer: 37

Step-by-step explanation:

Given : Significance level : $\alpha:1-0.98=0.02$

Critical value : $z_{\alpha/2}=z_{0.01}=2.33$

margin of error : E= 1 mile per gallon

Population standard deviation: $\sigma=2.6$ miles per gallon.

We know that when the population standard deviation is known then the formula to find the sample size is given by :

$n=(\dfrac{z_{\alpha/2}\times \sigma}{E})^2$

$n=(\dfrac{(2.33)\times 2.6}{1})^2=36.699364\approx37$ [Round to the next whole number.]

Hence, the required number of automobiles should be used in the test = 37

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3 years ago

Each side of the smaller square in the figure below is n inches long, and each side of the larger square is p inches longer than

lana66690 [7]

Answer:

2np + p²

Step-by-step explanation:

The general formula for the area of a square is A = s², where s = the length of one side of the square. In the case of the smaller square the area would be: n x n = n². Since the side of the larger square is 'p' inches longer, the length of one side is 'n + p'. To find the area of the larger square, we have to take the length x length or (n +p)².

Using FOIL (forward, outside, inside, last):

(n + p)(n+p) = n² + 2np + p²

Since the area of the first triangle is n², we can subtract this amount from the area of the larger square to find out how many square inches greater the larger square area is.

n² + 2np + p² - n² = 2np + p²

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3 years ago