The base of a triangle is 5cm greater than the height. The area is 18cm^2. Find the height and the base.
The height is triangle is?cm
The base of the triangle is?cm
a.$5.30
b.3,219
a.5.30
1) Let h represent the height. Then what is the length of the base, in terms of h?
2) For a triangle:
area = (1/2) * base * h
or
a = (1/2)bh
3) You are given the area, 18. So plug it in.
18 = (1/2)bh
4) Finally, in step (2) you found the length of the base, b, in terms of h. Plug that in for b. You now have only 1 variable, h, remaining in the equation, so you can solve to find the value of h.
5) Once you have h, you know the relationship between it and b, as determined in step (1). So it's just a matter of substitution to solve for b.
To find the height and base of the triangle, we can use the area formula for a triangle. The area (A) of a triangle is given by the formula A = 1/2 * base * height.
Let's assign variables to the base and the height of the triangle:
Let h be the height of the triangle.
Then, the base of the triangle is h + 5 cm.
Now, we can substitute the values into the area formula:
18 cm^2 = 1/2 * (h + 5 cm) * h
To solve for h, we can simplify and solve the quadratic equation.
Multiplying both sides by 2, we get:
36 cm^2 = (h + 5 cm) * h
Expanding the equation, we have:
36 cm^2 = h^2 + 5h cm
Rearranging the equation to bring everything to one side, we get:
h^2 + 5h cm - 36 cm^2 = 0
Now, we can solve this quadratic equation by factoring or by using the quadratic formula. Factoring this quadratic equation gives us:
(h + 9 cm)(h - 4 cm) = 0
Setting each factor to zero gives us two possible heights:
h + 9 cm = 0 or h - 4 cm = 0
Solving for h gives us:
h = -9 cm or h = 4 cm
Since the height of a triangle cannot be negative, we discard the negative value:
h = 4 cm
Now, we know the height (h) is 4 cm. To find the base, we substitute the value of h into the expression for the base:
Base = h + 5 cm
Base = 4 cm + 5 cm
Base = 9 cm
Therefore, the height of the triangle is 4 cm and the base is 9 cm.