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3 years ago

A triangle has two side lenths of 1 and 16 what is the largest possible whole-number length of the third side?

Mathematics

1 answer:

Afina-wow [57]3 years ago

6 0

Answer:

Step-by-step explanation:

Given that:

Length of two sides of the triangle = 1 and 16 ;

The largest possible whole-number length of the third side would be ;

Recall from triangle inequality theorem; the length of any two sides of a triangle is greater than the third side. Therefore. The largest possible whole number value the third side could have is:

Assume the third side is the largest :

Then, the third side must be less than the sum of the other two sides ;

Third side < (16 + 1)

Third side < 17

Therefore, the closest whole number lesser than the sum of the other two sides is (17 - 1) = 16

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3 years ago

The perimeter of a triangle is 35 feet. One side of the triangle is five feet longer than the second side. The third side is thr

Vaselesa [24]

Given:

The perimeter of the triangle = 36 feet.

Let the three sides of the triangle be x, y and z.

The measurements of the sides of the triangle are given by

$x=5+y$ and $z=3+y$

We need to determine the length of the sides.

Value of y:

Let us determine the value of y using the perimeter formula.

$Perimeter =x+y+z$

Substituting the values, we get;

$35=5+y+y+3+y$

$35=8+3y$

$27=3y$

$9=y$

Thus, the value of y is 9 feet.

Hence, the length of the second side is 9 feet.

Length of the sides:

Length of the 1st side is given by

$x=5+y$

$x=5+9$

$x=14$

Thus, the length of the first side is 14 feet.

Length of the third side is given by

$z=3+y$

$z=3+9$

$z=12$

Thus, the length of the third side is 12 feet.

Therefore, the length of the sides of the triangle are 14 feet, 9 feet and 12 feet.

6 0

3 years ago

What is the sum of the expressions (2/3x −7)+(1/3 x+5)?

Anit [1.1K]

The answer is

Final result :

x - 2
Step by step solution :

Step 1 :

1
Simplify —
3
Equation at the end of step 1 :

2 1
((—•x)-7)+((—•x)+5)
3 3
Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Adding a whole to a fraction

Rewrite the whole as a fraction using 3 as the denominator :

5 5 • 3
5 = — = —————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x + 5 • 3 x + 15
————————— = ——————
3 3
Equation at the end of step 2 :

2 (x + 15)
((— • x) - 7) + ————————
3 3
Step 3 :

2
Simplify —
3
Equation at the end of step 3 :

2 (x + 15)
((— • x) - 7) + ————————
3 3
Step 4 :

Rewriting the whole as an Equivalent Fraction :

4.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

7 7 • 3
7 = — = —————
1 3
Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

2x - (7 • 3) 2x - 21
———————————— = ———————
3 3
Equation at the end of step 4 :

(2x - 21) (x + 15)
————————— + ————————
3 3
Step 5 :

Adding fractions which have a common denominator :

5.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(2x-21) + (x+15) 3x - 6
———————————————— = ——————
3 3
Step 6 :

Pulling out like terms :

6.1 Pull out like factors :

3x - 6 = 3 • (x - 2)

Final result :

x - 2

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Hope This Helps! :)

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3 years ago

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kupik [55]