work this out ,if i have a right angle triangle with two sides of equal length and an area of 20cm squared wha

Question

ts the length of the third side?

also what are the two equal sides lengths?

Answer 1

let the equal sides be x
1/2x^2=area=20 given
x^2=40
x=rt40
using the pythagoras theorem
c^2=a^2+b^2
c=rt(a^2+b^2)
third side=rt(40+40)
=rt80
=4rt5 cm

Answer 2

The area of any triangle is 1/2 base x perpendicular height

(as the triangle is right angled, these 2 sides are mutually perpendicular)

Let base = height =L

20 (cm^2) = 1/2 L^2 (cm x cm)

[As a check, the dimensions work, cm x cm = cm^2]

40 = L^2

Now use Pythagoras's theorem

The square of the hypotenuse is equal to the sum of the squares of the other two sides.

The hypotenuse exists only in right angled triangles and is ALWAYS the side opposite the right angle

In this question, the other 2 sides are equal.

So the Hypotenuse squared is equal to L^2 +L^2

=2L^2, substituting L^2 = 40, 2L^2 = 80

The hypotenuse squared = 80

So the hypotenuse = square root of 80

The answer must be a little bit less than 9 as 9^2 = 81

You can work this out for yourself

Answer 3

To work this out we create two simultaneous equations and solve them. There are two variables x and y.

x is the length of the two sides of equal length
y is the length of the third side, the hypotenuse

Area of triangle is (x**2)/2 (a half of x squared)
By Pythagoras's theorem y**2 = x**2 + x**2 = 2x**2

Therefore the two equations are as follows
(x**2)/2 = 20 (therefore x**2 = 40)
y**2 = 2x**2

substitute for x in the second equation
y**2 = 80
y = sqrt(80)
y = 4 * sqrt(5)

Therefore length of third side is 4 * sqrt(5) (four times the square root of 5)

x**2 = 40
x = sqrt(40)
x = 2 * sqrt(10)

The length of the two other sides are 2 * sqrt(10) (twice the square root of 10)

Answer 4

Such an triangle's surface area would be :
S = (1/2) a ²
where a is the length of the 2 equal sides.

Therefore a ² = 40 cm ²
Pythagore tells us that the square of the 2rd side is 2a²
Its length is thus the square root of 80 or roughly 9 cm

Answer 5

The right triangle is clearly isosceles.
Area = 20 square cm
Let the triangle be ABC, right angled at B
Angle ABC = 90 degrees, AB = BC, AC is the hypotenuse.
Let AB and BC be 'x'(They are equal). AC is 'y'
As x is the height and x, the base,
x^2/2 = 20
x^2 = 40
2x^2 = 80_______________(i)

As y is the hypotenuse,
y^2 = x^2 + x^2
= 2x^2
y^2 = 80
y = sqrt80 ('sqrt' stands for square root of
= 4(sqrt5)
The length of the third side is 4(sqrt5) cm

From (i)
2x^2 = 80
x^2 = 40
x = sqrt40
= 2(sqrt10)
The length of each of the other two sides is 2(sqrt10) cm

Answer 6

For an isosceles rt triangle with legs=x
area is A=(1/2)x^2=20
x=2√5
the hypotenuse = leg*√2
si the sides are:

2√5
2√5
2√10

Answer 7

If the equal sides of the right triangle be p units each, the area must be half of a square having each side p; for the two equal sides must include the right angle between them, the other one, diagonal being the largest side. So p^2/2 = 20. This gives p = 2(root10) =6.32 units.The third side must be p(root2) = (6.32)(1.41)= 8.91.
is this OK ?
have nice fun.

Answer 8

If the two sides of a right triangle are equal, then each side is (the square root of forty) cm.

Then we apply that to the Pythagorean theorum. Asquared + Bsquared = Csquared.

Which would be 40 + 40 = Csquared.

The hypotenuse is (square-root-of-eighty) cm.

Answer 9

let x= the length of the
two equal sides

area =(1/2)x^2
20 =(1/2)x^2
>>x=sqrt(40) =2 sqrt(10)
=6.35 cm
let the third side =y=sqrt80
= 4 sqrt5
=8.95cm

i hope that this helps

Answer 10

If x is the length of one of the equal sides, then (x-squared)/2 is the area.

So (x-squared)/2 = 20, therefore
x = the square-root of 40

To get the length of the 3rd side (call it y), use Pythagoras:
x-squared plus x-squared = y-squared.

So y = the square-root of 80