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"}.
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Explanation:
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Area of a triangle: A = 1/2 * base * height = 1/2 * b * h ;

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

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

↔ 3 b² = 150 ;
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Now, divide EACH side of the equation by "3" ;
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→ 3 b² / 3 = 150 / 3 ;
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→ b² = 50 ;
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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
<span>_________________________________________________
</span>   → b =  √50
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→ √50 = √25 *√2 = 5√2
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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 ;
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  → round to 10.61 units .
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