SOLUTION: The three sides of a right triangle are proportional to another right triangle whose sides measure 3 cm, 4 cm, and 5 cm. Find the perimeter of the right triangle if its area is

Algebra ->  Triangles -> SOLUTION: The three sides of a right triangle are proportional to another right triangle whose sides measure 3 cm, 4 cm, and 5 cm. Find the perimeter of the right triangle if its area is      Log On


   



Question 1056340: The three sides of a right triangle are proportional to
another right triangle whose sides measure 3 cm, 4 cm, and 5 cm.
Find the perimeter of the right triangle if its area is 96 cm^2.

Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

The three sides of a right triangle

That's the one on the right.

are proportional to another right triangle
whose sides measure 3 cm, 4 cm, and 5 cm.

That's the one on the left.

The triangle on the right has sides whose lengths 
are some constant k times the lengths of the sides
of the triangle on the left. 

Find the perimeter of the right triangle if
its area is 96 cm^2.

The formula for the area of a triangle is

Area%22%22=%22%22expr%281%2F2%29base%2Aheight

For the larger triangle on the right, the area
is given as 96 cm², the base is 3k and the height
is 4k, so we substitute:

96%22%22=%22%22expr%281%2F2%293k%2A4k

96%22%22=%22%226k%5E2

18%22%22=%22%22k%5E2

sqrt%2818%29%22%22=%22%22k

sqrt%289%2A2%29%22%22=%22%22k

3sqrt%282%29%22%22=%22%22k

The perimeter is the sum of the three sides.

P%22%22=%22%223k+%2B+4k+%2B+5k

P%22%22=%22%2212k

P%22%22=%22%2212%2A3sqrt%282%29

P%22%22=%22%22matrix%281%2C2%2C36sqrt%282%29%2Ccm%29

Edwin

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The three sides of a right triangle are proportional to
another right triangle whose sides measure 3 cm, 4 cm, and 5 cm.
Find the perimeter of the right triangle if its area is 96 cm^2.
highlight_green%28matrix%281%2C4%2C+Perimeter%2C+%22=%22%2C+48%2C+cm%29%29