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4 years ago

The length of the hypotenuse of a 30°-60°-90° triangle is 7. Find the perimeter

2 answers:

6 0

Rules for a 30-60-90 right triangle:
hyp = 2 * short leg
Long leg = sqrt(3) * short leg
Given:
hyp = 7
7 = 2*short leg
divide both sides by 2
7/2 = short leg
long leg = sqrt(3) * short leg
long leg = sqrt(3) * (7/2)
long leg = 6.06
P= s1 + s2 + s3
P = 7 + 3.5 + 6.06
P = 16.56 units (Decimal approximation)
P = 10.5 + 3.5sqrt(3) units (Exact value)

Novosadov [1.4K]4 years ago

3 0

The shortest leg = 1/2 * 7 = 3.5
longest leg = 7 * sqrt 3 = 12.12

Perimeter = 7 + 3.5 + 12.12 = 22.62 to nearest hundredth

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ANEK [815]

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<h3>How to prove the equation?</h3>

The equation is given as:

$\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)$

Take the LCM

$\frac{(ax + by)(x - y) -(ax - by)(x + y)}{(x + y)(x - y)}= 2(a - b)$

Expand

$\frac{ax^2 - axy + bxy - by^2 -ax^2 - axy + bxy + by^2}{(x + y)(x - y)}= 2(a - b)$

Evaluate the like terms

$\frac{-2axy + 2bxy }{(x + y)(x - y)}= 2(a - b)$

Rewrite as:

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Factorize the numerator

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Divide

2(a - b)= 2(a - b)

Both sides are equal

Hence, the equation $\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)$ has been proved

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2 years ago

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Answer:

Step-by-step explanation:

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Step-by-step explanation:

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