The area of a right triangle is 17.5 c m 2 . One leg is 2cm shorter than the other. Find the length of the shortest side.The length of the shortest side is cm?

Question

The area of a right triangle is   17.5  c      m    2  . One leg is 2cm shorter than the other. Find the length of the shortest side.The length of the shortest side is cm?

Harper Brewer · Accepted Answer

The area of a triangle is given by bh/2. The legs of a right triangle have lengths that are the base and the height,fortunately. A=bh/2=17.5.bh=35.Let x=length of the shorter leg.x+2= length of the longer leg.x(x+2)=35      x    2    +  2  x  −  35  =  0  x  =            −      2      ±              4        +        140              2    =      5    ,    −    7  -7 is not a valid solution in real-world terms, though, since thereis no real-world concept of a negative area.So x=5, and the length of the shortest side is 5 cm.

equipokypip1 · Accepted Answer

We know that the area of a triangle is   A  =      1    2    b  hFor this problem we can exchange the B and H for x and x+2. Bysetting these variables = to this equation it is easy to solve forx. The x that we find in this equation will be the shorter leg.  17.5  =            (      x      )      (      x      +      2      )        2  Moving the 2 to the other side of the equation and distributing thex gives:  35  =      x          2        +  2  x     o  r         x          2        +  2  x  −  35  =  0Factoring this equation gives(x+7)(x-5)=0So this means that x=-7 or x=5.Since x can not be a negative number we know that the answer is 5.The shorter leg of the triangle is 5 cm long.

The area of a right triangle is 17.5cm^2. One leg is 2cm shorter than the other. Find the length of the shortest side.The length of the shortest side is cm?

Answered question

Answer & Explanation

New Questions in Trigonometry