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Ugo [173]
3 years ago
5

3.The legs of a right triangle are equal. Given the length of the legs, find the length of the hypotenuse. Round

Mathematics
1 answer:
Zepler [3.9K]3 years ago
3 0

Answer:

1.41a

Step-by-step explanation:

Let ABC is a right triangle with equal legs AB =BC.  

Hence, ∠B is 90° and CA is the hypotenuse.

Now, applying Pythagoras Theorem, we can write  

CA² = AB² + BC²

Let us assume that each legs AB = BC = a.

Therefore, CA² = a² +a² = 2a²

⇒Hypotenuse or CA = a√2 = 1.41a { Round to the nearest tenth} (Answer)

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Step-by-step explanation:

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Answer:

<u>Perimeter</u>:

= 58 m (approximate)

= 58.2066 or 58.21 m (exact)

<u>Area:</u>

= 208 m² (approximate)

= 210.0006 or 210 m² (exact)

Step-by-step explanation:

Given the following dimensions of a rectangle:

length (L) = \sqrt{252} meters

width (W) = \sqrt{175} meters

The formula for solving the perimeter of a rectangle is:

P  = 2(L + W) or 2L + 2W

The formula for solving the area of a rectangle is:

A = L × W

<h2>Approximate Forms:</h2>

In order to determine the approximate perimeter, we must determine the perfect square that is close to the given dimensions.  

13² = 169

14² = 196

15² = 225

16² = 256

Among the perfect squares provided, 16² = 256 is close to 252 (inside the given radical for the length), and 13² = 169 (inside the given radical for the width).  We can use these values to approximate the perimeter and the area of the rectangle.

P  = 2(L + W)

P = 2(13 + 16)

P = 58 m (approximate)

A = L × W

A = 13 × 16

A = 208 m² (approximate)

<h2>Exact Forms:</h2>

L = \sqrt{252} meters = 15.8745 meters

W = \sqrt{175} meters = 13.2288 meters

P  = 2(L + W)

P = 2(15.8745 + 13.2288)

P = 2(29.1033)

P = 58.2066 or 58.21 m

A = L × W

A = 15.8745 × 13.2288

A = 210.0006 or 210 m²

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3 years ago
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