How do you fine the area of a triangle given only the hypotenuse and the height or base?
A right triangle has a hypotenuse of length 10 and a leg of length 7. What is the area of the triangle?
Please tell me how to solve this problem? 
Hello!
A=1/2bh
We need to know the base and height.
If we’re given the base and height, we can multiply it and divide by 2 (:
For your question:
We need to find the base for your question.
We use Pythagorean Theorem:
a^2+b^2=c^2
7^2+b^2=10^2
49+b^2=100
b^2=51
b=√51
b=7.141428429
The base would be around 7
So now we apply the formula:
A=1/2(7)(7)
A=24.5
Hope this helps!
Sincerely,
Mr.Math
Message me if you need more help.
We need to find the other length of the triangle first.
By pythagoras, b^2 + 7^2 = 10^2
b = sqrt(100 – 49)
b = sqrt(51)
Then area = 0.5 x base x height
= 0.5 x sqrt(51) x 7
= (7/2)sqrt(51) square units, or approx 25 square units of area
References :
a² + b² = c²
7² + b² = 10²
49 + b² = 100
b² = 51
b = √51
Now that you know the length of the third side, the area of a triangle formula is A = 1/2bh
A= 1/2 (√51) (7)
A= 3.5(√51)
A = 3.5(7.14142843)
A = 24.9949995, or about 25.
References :
Hello!
A=1/2bh
We need to know the base and height.
If we’re given the base and height, we can multiply it and divide by 2 (:
For your question:
We need to find the base for your question.
We use Pythagorean Theorem:
a^2+b^2=c^2
7^2+b^2=10^2
49+b^2=100
b^2=51
b=√51
b=7.141428429
The base would be around 7
So now we apply the formula:
A=1/2(7)(7)
A=24.5
Hope this helps!
Sincerely,
Mr.Math
Message me if you need more help.
References :