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Romashka-Z-Leto [24]
3 years ago
7

A triangle has a base that is 4cm longer than its height.

Mathematics
1 answer:
il63 [147K]3 years ago
5 0

Answer:

a) A =( x^2 -4x)/2

b) 16 cm^2

Step-by-step explanation:

Let the base of the triangle be x cm

since it is longer, then the height would be (x-4) cm

Mathematically, the area of a triangle is the product of the base and the height divided by 2

So, we have this as;

A = 1/2(x-4)x

A = x(x-4)/2

A = (x^2 - 4x)/2

A =( x^2 -4x)/2

To find the area, we only need to substitute 8 cm for x

we have this as;

A = (8^2 -4(8))/2

A = (64-32)/2 = 32/2 = 16 cm^2

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Based on my experiences so far, the approach to geometry that I prefer is: Euclidean Geometry. This is because the problems are easy to visualize since they are restricted to two-dimensional planes.

<h3>Which approach is easier to extend beyond two dimensions?</h3>

The approach that is easier to extend beyond two dimensions is Euclidean Geometry. Again, this is because of how it deals with shapes and visualization of the same.

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2 years ago
How many real solutions exist for this system of equations? y = x^2 + 4 y = 4x
-BARSIC- [3]

Answer:

This system of equations has one real solution, (2, 8).

Step-by-step explanation:

Given:

y = x² + 4

y = 4x

1. Substitute the given value of y into y = x² + 4:

⇒ 4x = x² + 4

2. Solve for x (by factoring):

⇒ 4x = x² + 4

⇒ 0 = x² - 4x + 4

⇒ 0 = (x - 2)² [perfect square rule: a² -2ab + b² = (a - b)²]

⇒ 0 = (x - 2)² [take the square root of both sides]

⇒ \sqrt{0} = \sqrt{(x - 2)^2}

⇒ 0 = x - 2 [add 2 to both sides]

⇒ 0 + 2 = x - 2 + 2

⇒ 2 = x

3. Find the value of y by substituting the given value of x into y = 4x:

⇒ y = 4(2)

⇒ y = 8

4. Check your work:

⇒ y = x² + 4          and          ⇒ y = 4x

⇒ 8 = 2² + 4         and          ⇒ 8 = 4(2)

⇒ 8 = 4 + 4          and           ⇒ 8 = 8 ✔

⇒ 8 = 8 ✔

Solution: (x, y) ⇒ (2, 8)

Learn more about solving system of equations:

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