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Alecsey [184]
3 years ago
14

A triangle has one side length of 12 inches and another of 8 inches. Describe all possible lengths of the third side. Show and e

xplain your reasoning.
Mathematics
2 answers:
Vinvika [58]3 years ago
6 0

Answer:

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

Step-by-step explanation:

we know that

<u>The Triangle Inequality Theorem</u> states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let

c----> the length of the third side of triangle

Applying the triangle inequality theorem

1) 12+8 > c

20 > c

Rewrite

c < 20 in

2) 8+c > 12

c > 12-8

c < 4 in

therefore

4 in < c < 20 in

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

katrin [286]3 years ago
5 0

Answer:

The third side must be smaller than 20 inches and greater than 4 inches

4

Step-by-step explanation:

Let a, b and c be the lengths of triangle's sides. Then

a+b>c\\ \\a+c>b\\ \\b+c>a

Use this rule in your case. So, if a=12 and b=8, then

12+8>c\\ \\12+c>8\\ \\8+c>12

Hence, you get

c-4\\ \\c>4

From these inequalities, you can state that

4

So, c must be smaller than 20 inches and greater than 4 inches.

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2 \sqrt{98} \cdot \sqrt{2} =2 \sqrt{49\times2} \cdot \sqrt{2}  \\  \\ =2 \sqrt{49} \cdot \sqrt{2} \cdot \sqrt{2} =2\times7\times2 \\  \\ =28
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3 years ago
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kicyunya [14]

Answer:

B.

Step-by-step explanation:

4 0
2 years ago
The difference 2/5(d−10)−2/3(d+6) is
spin [16.1K]

Let's simplify step-by-step.

2/5(d−10)−2/3(d+6)

Distribute:

= (2/5)(d)+(2/5)(−10)+ −2/3d+ −4

= 2/5d+−4+ −2/3d+ −4

Combine Like Terms:

= 2/5d+−4+ −2/3d+ −4

= −4/15d+−8

And your answer is...

= −4/15d+−8

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6 0
3 years ago
Read 2 more answers
1. A soccer field has an area (A = LW) that is represented by the polynomial 1 point
matrenka [14]

Answer:

(x + 6)(x - 6)

Step-by-step explanation:

Given

See attachment for soccer field

Required

The possible dimension of the field

From the attachment, we have:

Area = x^2 - 36

Length = x +a

Width = x + b

So, we have:

Length * Width = Area

This gives:

(x + a)(x + b) = x^2 - 36

Express 36 as 6^2

(x + a)(x + b) = x^2 - 6^2

Express as difference of two squares

(x + a)(x + b) = (x + 6)(x - 6)

Hence, the dimension is: (x + 6)(x - 6)

6 0
2 years ago
Nandini makes 'halwa' one evening and divides it into four equal portions for her family of four. However, just as they are abou
wel

Answer:

5%

Step-by-step explanation:

Total 'halwa' made = 1

Divided into four equal portion = 1/4

Arrival of an unexpected guest = 1/5

By what percentage has each family member's share been reduced:

Change in the sharing proportion:

Previous share ratio - new sharing ratio

(1/4 - 1/5) = (5 - 4) / 20 = 1/20

That means total reduction in the sharing = 1/ 20

Since each member comes contributed equally:

Reduction in each family member's share ;

(1 / 20) ÷ 4

(1 / 20) * 1/4 = 1/ 80

Percentage reduction:

(Reduction / original share) * 100%

[(1/80) ÷ (1/4)] * 100

(1/80 * 4/1) * 100%

(1/20) * 100%

= 5%

Reduction in each family members share = 5%

3 0
2 years ago
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