In a right triangle, one of the legs is 5 cm smaller than the hypotenuse, and the other leg is 10 cm smaller than the hypotenuse. Find the length of the hypotenuse

Guest Mar 11, 2020

#1**+2 **

In a right triangle, one of the legs is 5 cm smaller than the hypotenuse, and the other leg is 10 cm smaller than the hypotenuse. Find the length of the hypotenuse

(x+5)^{2}+(x+10)^{2}=(x+15)^{2}

Step 1: Simplify both sides of the equation.

2x^{2}+30x+125=x^{2}+30x+225

Step 2: Subtract x^{2} from both sides.

2x^{2}+30x+125−x^{2}=x^{2}+30x+225−x^{2}

x^{2}+30x+125=30x+225

Step 3: Subtract 30x from both sides.

x^{2}+30x+125−30x=30x+225−30x

x^{2}+125=225

Step 4: Subtract 125 from both sides.

x^{2}+125−125=225−125

x^{2}=100

x = 10

*sqrt [(10+5) ^{2} + (10+10)^{2}] = 25 cm *

Dragan Mar 11, 2020