All categories

3 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]3 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]3 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 .
_______________________________________________________

You might be interested in

Jeff feeds the family dog on Wednesdays and his sister Melody feeds the dog on Fridays. On Wednesday, Jeff gave the dog 5/8 of a

Tasya [4]

8 x 5/8 = The ounces fed by Jeff
You need to convert 1/2 with the denominator of 8 with would be 4/8
8 x 4/8 = The ounces fed by Melody
HOPE THIS HELPS!!

4 0

3 years ago

Please im desperate please help me

g100num [7]

A is your answer tell me if I am wrong.

5 0

3 years ago

Identify the solution and graph of the given inequality. p 5/14 p < 4/7

Dvinal [7]

Answer:

p > 5/14

Step-by-step explanation:

4 0

3 years ago

Identify an equation in point-slope form for the line parallel to y = 1*-7 that

kakasveta [241]

Answer:

y + 2 = 1 (x+3) ............> y + 2 = x + 3

Explanation:

The general form of the equation of a line in point-slope form is:

y - y₁ = m (x - x₁)

where:

m is the slope of the line

(x₁ , y₁) is a point that belongs to the line

The general form of the equation of a line in slope-intercept form is:

y = mx + c

where:

m is the slope

c is the y-intercept

1- Getting the point:

We are already given the point (-3 , -2) so we'll directly use it

2- Getting the slope

We are given that our line is parallel to the line:

y = 1x - 7

We know that parallel lines have equal slopes

This means that:

slope of the line we want = 1

3- Getting the equation:

Substitute with the point and slope in the above form to get the equation

This is done as follows:

y - y₁ = m (x - x₁)

y - (-2) = 1 (x - (-3))

y + 2 = 1 (x + 3)

y + 2 = x + 3

Hope this helps :)

4 0

3 years ago

Given the graphs of f(x) = -x + 2 and g(x) = 5x – 4, what is the solution to the equation f(x) = g(x)?

Stels [109]

Answer:

c) 1

Step-by-step explanation:

f(x) = g(x)

-x+2 = 5x-4

+x +x

2 = 6x -4

+4 +4

6 = 6x

(divide both sides by 6)

1 = x

7 0

3 years ago

Read 2 more answers