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2 years ago

The base of the triangle is one and a half times it's height. what is height if area is 75

Mathematics

2 answers:

Setler [38]2 years ago

8 0

H=15cm
b=10cm
i think, i asked my mom thats a teacher and she said it was correct.

Margarita [4]2 years ago

8 0

Answer: The height is: 10.61 units.
{or, write as: "(7.5 √2) units"}.
_____________________________________________________
Explanation:
_____________________________________________________
Area of a triangle: A = 1/2 * base * height = 1/2 * b * h ;

Given: b = 1.5 * h ;
A = 75 units²
______________________________
Solve for "h" ("height") ; h = 1.5 b ;
_________________________________
So, we solve for "b" ; then we plug that value into the equation:

→ h = 1.5 b ; to get the height, "h" ;
______________________________________________________
→ 75 = 1/2 * (b) (1.5 b) ;
______________________________________________________
Multiply the ENTIRE equation by "2" ;
to get rid of the fraction and decimals ;
______________________________________________________
→ 2 * { 75 = 1/2 * (b) (1.5 b) } ;
______________________________________________________
→ 150 = b * 3b ;
______________________________________________________
→ 150 = 3 b² ;

↔ 3 b² = 150 ;
______________________________________________________

Now, divide EACH side of the equation by "3" ;
_________________________________________________
→ 3 b² / 3 = 150 / 3 ;
_________________________________________________
→ b² = 50 ;
_________________________________________________
Now, take the POSITIVE square root of each side of the equation;
to isolate "b" on one side of the equation; and to solve for "b" ;
_________________________________________________
 → √(b²) = √50
_________________________________________________
 → b = √50
_________________________________________________
→ √50 = √25 *√2 = 5√2
_________________________________________________
h = (1.5) b = (1.5) *(5) (
_____________________________________________________
Explanation:
_____________________________________________________
Area of a triangle: A = 1/2 * base * height = 1/2 * b * h ;

Given: b = 1.5 h ;
A = 75 units²
______________________________
Solve for "h" ("height") ; h = 1.5 b ;
_________________________________
So, we solve for "b" ; then we plug that value into the equation:

→ h = 1.5 b ; to get the height, "h" ;
______________________________________________________
→ 75 = 1/2 * (b) (1.5 b) ;
______________________________________________________
Multiply the ENTIRE equation by "2" ;
to get rid of the fraction and decimals ;
______________________________________________________
→ 2 * { 75 = 1/2 * (b) (1.5 b) } ;
______________________________________________________
→ 150 = b * 3b ;
______________________________________________________
→ 150 = 3 b² ;

↔ 3 b² = 150 ;
______________________________________________________

Now, divide EACH side of the equation by "3" ;
_________________________________________________
→ 3 b² / 3 = 150 / 3 ;
_________________________________________________
→ b² = 50 ;
_________________________________________________
Now, take the POSITIVE square root of each side of the equation;
to isolate "b" on one side of the equation; and to solve for "b" ;
_________________________________________________
 → √(b²) = √50
_________________________________________________
 → b = √50
_________________________________________________
 → b = √50 = √25 *√2 = 5√2
_________________________________________________
→ h = 1.5 * 5 * √2 ;
_________________________________________________
→ h = (7.5 √2) units ;

or, (7.5) * (√2) = 10.6066017177982129 units ;
_______________________________________________________
 → round to 10.61 units .
_______________________________________________________

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So, Null Hypothesis, $H_0$ : $p_1\leq p_2$ {means that the percentage of employed workers who have registered to vote does not exceeds the percentage of unemployed workers who have registered to vote}

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where, $\hat p_1$ = sample proportion of employed workers who have registered to vote = $\frac{287}{513}$ = 0.56

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So, the test statistics = $\frac{(0.56-0.46)-(0)}{\sqrt{\frac{0.56(1-0.56)}{513}+\frac{0.46(1-0.46)}{604} } }$

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The value of z test statistics is 3.349.

Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.

Since our test statistic is more than the critical value of z as 3.349 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.

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