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Setler [38]
2 years ago
6

If the square of the hypotenuse of an isosceles right triangle is 128 cm2, find the length of each side.​

Mathematics
2 answers:
kotegsom [21]2 years ago
5 0
<h3>⋆Solution:</h3>

<u>Let the two equal side of right angled isosceles triangle, right angled at Q be k cm.</u>

⋆ Given: h2 = 128

<u>So, we get</u>

\small\bold{PR2 = PQ2 + QR2}

\small\bold{h2 = k2 + k2 }

\small\bold\pink{ ⇒ }\small\bold{ 128 = 2k2 }

\small\bold\pink{ ⇒ }\small\bold{\frac{128}{2} = k2 }

\small\bold\pink{ ⇒ }\small\bold{ 64 = k2}

\small\bold\pink{ ⇒ }\small\bold{ \sqrt{64} = k}

\small\bold\pink{ ⇒ }\small\bold{8 = k }

<u>Therefore, length of each side is 8 cm.</u>

denis-greek [22]2 years ago
3 0

Answer:

<u>8 cm</u>

Step-by-step explanation:

Let the length be l.

Then, by Pythagorean Theorem,

l² + l² = 128

2l² = 128

l² = 64

l = <u>8 cm</u>

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Anvisha [2.4K]

Answer:

x = 18; y = 20

Step-by-step explanation:

6.

Triangles KLM and KNO are similar, so the ratios of the lengths of corresponding sides are equal.

KL/KN = LM/NO

10/30 = 6/x

Cross multiply.

10x = 6 * 30

10x = 180

x = 18

KL + LN = KN

10 + y = 30

y = 20

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3 years ago
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diamong [38]

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Reptile [31]

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47 degrees

Step-by-step explanation:

Add all the numbers we know

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A square field has an area of 144 metres squared. If Andrea walked 10 times around this field, what distance did she cover?
Novosadov [1.4K]

Answer:

480m

Step-by-step explanation:

First we have to find the perimeter of the field.

We know that the area is 144m and that the field is a square.

Since a squares sides are all equal, we can do \sqrt{144}, which is 12m.

So, one side of the field is 12m; now we just find the perimeter which is easy since its a square. 12*4=48m

If Andrea walked around it 10 times, then we just multiply the perimeter by 10

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7 0
3 years ago
If f(x)f(x) is an exponential function where f(-1)=5f(−1)=5 and f(7)=32f(7)=32, then find the value of f(4)f(4), to the nearest
Whitepunk [10]

Using an exponential function, it is found that the value of the function when x = 4 is of f(4) = 15.95.

<h3>What is an exponential function?</h3>

It is modeled by:

y = ab^x

In which:

  • a is the initial value.
  • b is the rate of change, as a decimal.

In this problem, we have that f(-1)=5, hence:

5 = ab^{-1}

\frac{a}{b} = 5

a = 5b

We also have that f(7)=32, hence:

32 = ab^7

Since a = 5b:

5b^8 = 32

b = \sqrt[8]{\frac{32}{5}}

b = 1.2612.

a = 5b = 5 x 1.2612 = 6.306.

Hence the function is given by:

y = 6.306(1.2612)^x

Then, when x = 4, we have that:

y = 6.306(1.2612)^4 = 15.95

More can be learned about exponential functions at brainly.com/question/25537936

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