area of a right triangle?

Question

the sides are 2x (height), x (width), and the hypotenuse is 10. the answer is 20 but how do i work it out? the formula is a=1/2(ht * width)

Answer 1

Use pythagorean theorem
(2x)^2 + x^2 = 10^2
4x^2 + x^2 = 100
5x^2 = 100
x^2 = 20
x = sqrt(20)
x = 2sqrt(5)
Area = (1/2)(2x)(x)
= (1/2)(2*2sqrt(5))(2sqrt(5))
= (1/2)(4*2*5)
= 20

Answer 2

2x, x, 10.

You don't even have the answer!

The question is to find x.

To do this, you need the pythagorean theorem.

so make b be the base and h be the height.

h = 2b, so 4b^2 + b^2 = 100.

This means that 5b^2 = 100, or b^2 equals 20. So b equals sqrt(20) and h equals 2sqrt(20), or sqrt(80).

But now for the area. ( 2sqrt(20) * sqrt(20) ) / 2 equals 20, so no need to worry about that.

Answer 3

Use the theorem of phythagoras. Lets labell you width A and Height B, and your hypotonuse C

Heres the formulea: Csquared= Asquared + Bsquared

Lets say your answer d, you take d and find the square root then you got the length of your hypotenude

Answer 4

First us pythagoras theorem:
(2x)*(2x)+(x)*(X)=10*10
4x^2(read as 4x squared)+x^2=100
5x^2=100
x^2=20
x(width)=square root of 20=2 root 5
2x(height)=2*(2 root 5)=4 root 5
a=1/2(ht*width) =1/2*4 root 5* 2root 5=20
thus your answer has come.

Answer 5

right triangle with sides a,b and c where c is the hypotenuse

You know that
c² = a² + b² (pythagorean theorem)
and
A = ab/2

but
a = 2x
b = x
c = 10
so
10² = (2x)² + (x)²
100 = 4x² + x²
5x² = 100
x² = 20

A = ab/2 but a = 2x and b = x so
A = (2x)(x)/2
A = x²
but x² = 20 so
A = 20

^_^

Answer 6

consult your text book