Maths Problem?

Question

I am doing a math assignment and I cant' remember how to work out a problem. I have the area of a right angle triangle which is 19.25 sq m and one side is xm the other x+4m and need to write an expression in terms of x

Answer 1

Area = 0.5 x base x height
= 0.5 x (x) x (x + 4)
= 0.5 x^2 (2x) = 19.25
= x^2 + 4x - 38.50 = 0
x = 4.519202405 (+ve value only)

Hope this helps and vote for it if it turns you on!

Answer 2

The area of a triangle (any triangle, right or otherwise) is 1/2 base times height.

Area = 1/5 * base * height

We know that
Area = 19.25
base = x meters
height = x + 4 meters

(Because the sides of a right triangle are the base & height)

So,

A = 1.5 * b * h
19.25 = 1.5 * x * (x +4): Expression in terms of x

Expression in terms of x - other simplified versions

19.25 = 1.5 (x^2 + 4x)
19.25 = 1.5x^2 + (1.5)(4x)
19.25 = 1.5x^2 + 6x
1.5x^2 + 6x = 19.25 -------> Answer I would submit*
1.5x^2 + 6x - 19.25 = 19.25 - 19.25
1.5x^2 + 6x - 19.25 = 0 : Std Form of a Quadratic

Can solve for x using the Quadratic Formula

A = 1.5 B = 6 C = -19.25

Formula

x = -b +/- the square root of (b^2-4ac) divided by 2a


* If I was only asked to write an expression in terms of x

Answer 3

Are those the two sides that form the right angle?
I presume they are...
In which case you need to imagine a rectangle with these sides would be area of [x multiplied by (x+4)]
...and therefore a triangle with these two sides, and the third side being the diagonal across the center of the aforesaid rectangle must be exactly HALF of the area...

so [x multiplied by (x+4)] all divided by 2 (ie half) is the area of the triangle:

Therefore:

[X x (X+4)] / 2 = area of triangle
(you have to do the last bit yourself ;-)

Answer 4

assuming both sides form the right angle,

formula for area of a triange:
1/2 (x) (x+4) = 19.25
(x^2 + 4x) = 38.5
x^2 + 4x - 38.5 = 0 ---> expression in terms of x

Answer 5

1/2 * x * x+ 4

Answer 6

You do not know exactly whether the two sides are at right angles to each other.
So let us start from the area.

If the two areas are at rt angles, then the area =

1/2 *(x)*(X+4) = 19.25
You can find x from this.
Using the Pythagoras theorem you can find the third side.

Once you find the third side, verify using hero's formula

Area = sqrt (s(s-a)(s-b)(s-c)) where s= 9a+b+c)/2

If it matches, our assumption is correct. Otherwise, we have to consider X+4 as hypotenuse and continue.

Answer 7

how do you get the area of the right triangle?

(1/2) *base*height

you dont need to find the hypotenuse.. or c

the base or height are. the legs.. which are.. x and x+4

so (1/2) (x)(x+4)

(x² +4x)/2= 19.25

you equate it to the area given :)

multiply 2 to both sides.. thus cancelling the 2 on the left part

x² +4x = 38.5

x² +4x-38.5=0

use the quadratic formula to find x

-b +-√b^2 -4ac .. all over.. 2a

then substitute..

since you didnt say .. FIND X.. im not gonna solve it anymore? :)

Answer 8

Assume the sides are at right angles to one another.
(1/2) .X.(X + 4) = 19.25
X.(X + 4) = 38.5
X² + 4X - 38.5 = 0
This is an expression in X as required by the stated question.

Answer 9

A = 19.25m² = (leg1*leg2)/2

leg1 = x
leg2 = x+4

thus A = (x*(x+4))/2 = (x²+4x)/2
(x²+4x)/2 = 19.25 |*2
x² + 4x = 48.5
x² + 4x - 48.5 = 0
x1 = (-4 + sqrt(4² - 4*(-48.5)))/2 = 5.24568837
x2 = (-4 - sqrt(4² - 4*(-48.5)))/2 = -9.24568837

a leg can't have a negative length => x1
leg1 = 5.24568837
leg2 = 5.24568837 + 4 = 9.24568837

Answer 10

1/2[x*(x+4)]=19.25