MATH SOLVE

4 months ago

Q:
# The height of a triangle is 9 m less than it’s base. The area of the triangle is 56m 2. Find the length of the base

Accepted Solution

A:

Hi there! The answer is 16 meters.

To find our answer, we must set up and solve an equation.

First step: Set up an expression

Let the base of the triangle be represented by x.

Now we can conclude that the heigth of the triangle can be expressed by the expression x - 9 (since the height is 9m less than it's base).

Second step: Find the area, expressed in terms of x.

The area of a triangle can be found using the following formula

A = base * height * 0.5

(or A = (base * height) / 2)

When we plug in our data, we can find an expression of the area. We express the area in terms of x.

[tex]A = 0.5x(x-9)[/tex]

Step 3: Simplify

[tex]A = 0.5x(x-9)[/tex]

Work out the parenthesis using rainbow method.

[tex]A = 0.5x^{2} - 4.5x[/tex]

Step 4: Set up and solve the equation

When we've found our area expressed in terms of x, we can set up an equation.

[tex]0.5 x^{2} -4.5x = 56[/tex]

Subtract 56

[tex]0.5 x^{2} -4.5 - 56=0[/tex]

Divide by 2.

[tex] x^{2} - 9 x- 112 = 0 [/tex]

[tex](x+7)(x-16) = 0[/tex]

Rule AB = 0, gives A = 0 or B = 0

[tex]x + 7 = 0 \\ x = -7\\ \\ x - 16 = 0\\ x = 16 [/tex]

Step 5: Conclusion

The length of the base of the triangle (which was represented by x) is 16 metres (it can't be -7, since that's a negative number and length can't be negative).

The answer is 16 meters.

~ Hope this helps you!

To find our answer, we must set up and solve an equation.

First step: Set up an expression

Let the base of the triangle be represented by x.

Now we can conclude that the heigth of the triangle can be expressed by the expression x - 9 (since the height is 9m less than it's base).

Second step: Find the area, expressed in terms of x.

The area of a triangle can be found using the following formula

A = base * height * 0.5

(or A = (base * height) / 2)

When we plug in our data, we can find an expression of the area. We express the area in terms of x.

[tex]A = 0.5x(x-9)[/tex]

Step 3: Simplify

[tex]A = 0.5x(x-9)[/tex]

Work out the parenthesis using rainbow method.

[tex]A = 0.5x^{2} - 4.5x[/tex]

Step 4: Set up and solve the equation

When we've found our area expressed in terms of x, we can set up an equation.

[tex]0.5 x^{2} -4.5x = 56[/tex]

Subtract 56

[tex]0.5 x^{2} -4.5 - 56=0[/tex]

Divide by 2.

[tex] x^{2} - 9 x- 112 = 0 [/tex]

[tex](x+7)(x-16) = 0[/tex]

Rule AB = 0, gives A = 0 or B = 0

[tex]x + 7 = 0 \\ x = -7\\ \\ x - 16 = 0\\ x = 16 [/tex]

Step 5: Conclusion

The length of the base of the triangle (which was represented by x) is 16 metres (it can't be -7, since that's a negative number and length can't be negative).

The answer is 16 meters.

~ Hope this helps you!