Answer :
Sure! Let's solve the problem step by step.
We are given a right triangle where the height is 4 times the length of the base and the area of the triangle is 800. We need to find the height.
1. Let the length of the base be [tex]\( b \)[/tex].
2. Thus, the height [tex]\( h \)[/tex] is [tex]\( 4b \)[/tex] (since the height is 4 times the base).
3. The formula for the area of a triangle is:
[tex]\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\][/tex]
4. Substitute the known values into the formula:
[tex]\[
800 = \frac{1}{2} \times b \times 4b
\][/tex]
5. Simplify the equation:
[tex]\[
800 = 2b^2
\][/tex]
6. Solve for [tex]\( b^2 \)[/tex]:
[tex]\[
b^2 = \frac{800}{2} = 400
\][/tex]
7. Take the square root of both sides to solve for [tex]\( b \)[/tex]:
[tex]\[
b = \sqrt{400} = 20
\][/tex]
8. Since the height [tex]\( h \)[/tex] is 4 times the base:
[tex]\[
h = 4 \times b = 4 \times 20 = 80
\][/tex]
So, the height of the triangle is [tex]\(\boxed{80}\)[/tex].
We are given a right triangle where the height is 4 times the length of the base and the area of the triangle is 800. We need to find the height.
1. Let the length of the base be [tex]\( b \)[/tex].
2. Thus, the height [tex]\( h \)[/tex] is [tex]\( 4b \)[/tex] (since the height is 4 times the base).
3. The formula for the area of a triangle is:
[tex]\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\][/tex]
4. Substitute the known values into the formula:
[tex]\[
800 = \frac{1}{2} \times b \times 4b
\][/tex]
5. Simplify the equation:
[tex]\[
800 = 2b^2
\][/tex]
6. Solve for [tex]\( b^2 \)[/tex]:
[tex]\[
b^2 = \frac{800}{2} = 400
\][/tex]
7. Take the square root of both sides to solve for [tex]\( b \)[/tex]:
[tex]\[
b = \sqrt{400} = 20
\][/tex]
8. Since the height [tex]\( h \)[/tex] is 4 times the base:
[tex]\[
h = 4 \times b = 4 \times 20 = 80
\][/tex]
So, the height of the triangle is [tex]\(\boxed{80}\)[/tex].
