# I need help with this "the area of a riight angle triangle is 210 square meters if the hypotanure is 37 meters long find the lenght and altitude."the problem i am having here is that i know xy=210...

I need help with this "the area of a riight angle triangle is 210 square meters if the hypotanure is 37 meters long find the lenght and altitude."

the problem i am having here is that i know xy=210 as its the area and (37)2=x2+y2 according to pythagorus theoram but i cant get the answer right.

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### 2 Answers

You need to come up with the notation for the legs of triangle such that x represents one leg and y the other leg.

You need to remember that the area of a right angle triangle is half of product of legs of triangle such that:

`A = (xy)/2`

The problem provides the information that area of triangle is of `210 m^2` such that:

`210 = (xy)/2 =gt 420 = xy`

The problem provides the information that the hypotenuse of triangle is of 37 m, hence you may use Pythagorean theorem such that:

`x^2 + y^2 = 37^2`

You need to use the equation `420 = xy` to write x in terms of y such that:`x = 420/y.`

`(420/y)^2 + y^2 = 37^2`

You need to bring these terms to a common denominator such that:

`420^2 + y^4 - 37^2y^2 = 0`

You should come up with the notation `y^2 = z` such that:

`z^2 - 37^2z - 420^2 = 0`

`z_(1,2) = (37^2 +- sqrt(37^2 + 4*420^2))/2`

`z_(1,2) = (37^2 +- sqrt(1369 + 4*420^2))/2`

`z_(1,2) = (37^2 +- sqrt706969)/2`

`z_(1,2) = (37^2 +-840.814)/2`

`z_(1,2) = (1369 +-840.814)/2 =gt z_1 = 1104.907`

Since `z = y^` 2, the second negative value for z is not accepted.

`y = sqrt1104.907 =gt y = 33.24 m`

You need to keep only positive value for y.

`x = 420/33.24 =gt x = 12.63 m`

**Hence, evaluating the lengths of legs of triangle yields x = 12.63m and y = 33.24 m.**

This might help.

In the triangle if

x = lenght and y = altitude

then xy/2 = 210

because the area of a triangle is altitude times base divided by two.