The hypotenuse of a right triangle is 40 cm. One of the legs is 8 cm longer than the other leg. Find the area of the triangle in square feet.

Question

The hypotenuse of a right triangle is 40 cm. One of the legs is 8 cm longer than the other leg. Find the area of the triangle in square feet. Its a right triangle and the answer must be 384 I just want to know how to get that answer please

Answer 1

a² + b² = c²

 

Let x = the length of one leg, the second leg is x+8, therefore:

 

x² + (x+8)² = 40²

 

x² + x² + 16x + 64 = 1600

 

2x² + 16x - 1536 = 0

 

x² + 8x - 768 = 0

 

(x+24)(x-16) = 0

 

x = -24 or x = 16

 

16 is the only answer that works

Answer 2

I like Thomas' answer. However if we start at 16 for the short side and add 8 we get 24 for the long side.  16 squared is 256. 24 squared is 576. add them together and you get 832 not 1600. It turns out 16 times 24 is 384 (not 786). It turns out he 2 factors of 768 we are looking for are 24 and 32. 24 is the only answer.

 

So the sides of the triangle are 24, 32 and 40 (a 3 4 5 right triangle.)

 

The area for a triangle is A=1/2 bh. So for this triangle A=1/2 (24)(32) = 1/2 768 = 384 cm² 

 

Hope this helps. If not let me know.