The base of a trianglr is 8cm greater then the hight. the area is 64cm ^2 find the hight and the length of the base.
I get the answer as Hight is 8 cm and the base 16 I hape this is correct?
height = x base = x+8
Area = 1/2 hb
64 = 1/2x (x+8)
Solve for x, then x+8.
X=8 then 8+8 is 16
To find the height and length of the base of the triangle, we can use the formula for the area of a triangle, which is 1/2 * base * height.
Given that the area is 64 cm^2, we can set up the equation:
1/2 * base * height = 64
Since the base is 8 cm greater than the height, we can express the base as h + 8:
1/2 * (h + 8) * h = 64
To solve this equation, we need to rewrite it in a simpler form:
(h + 8) * h = 128
Expanding the equation:
h^2 + 8h = 128
Rearranging the equation:
h^2 + 8h - 128 = 0
Now, we can solve this quadratic equation. Factoring it would be difficult in this case, so we can use the quadratic formula:
h = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 8, and c = -128. Plugging these values into the formula:
h = (-8 ± √(8^2 - 4(1)(-128))) / (2(1))
Simplifying further:
h = (-8 ± √(64 + 512)) / 2
h = (-8 ± √(576)) / 2
h = (-8 ± 24) / 2
Now, we get two possible values for the height:
h = (-8 + 24) / 2 = 16/2 = 8 cm
or
h = (-8 - 24) / 2 = -32/2 = -16 cm
Since the height of a triangle cannot be negative, we discard the negative value.
Therefore, the height of the triangle is 8 cm.
Now, to find the length of the base, we can substitute the value of the height back into the equation for the base:
base = height + 8
base = 8 + 8
base = 16 cm
Therefore, the length of the base is 16 cm.