MATHEMATICS MIDDLE SCHOOL

The shorter leg of a right triangle is 6 feet shorter than the longer leg. The hypotenuse is 6 feet longer than the longer leg. Find the side lengths of the triangle.

Answers

Answer 1
Answer:

The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.

Step-by-step explanation:

Let,

Longer leg = a = x

Shorter leg = b = x - 6

Hypotenuse = c = x + 6

As the triangle is right angles, therefore, using pythagoras theorem;

a^2+b^2=c^2\n(x)^2+(x-6)^2=(x+6)^2\nx^2+(x^2-12x+36)=x^2+12x+36\nx^2+x^2-12x+36=x^2+12x+36\n 2x^2-12x+36=x^2+12x+36

Adding (-x² - 12x-36) on both sides

2x^2-12x+36-x^2-12x-36=x^2+12x+36-x^2-12x-36\nx^2-24x=0

Taking x common;

x(x-24)=0\n

Either,

x=0

or,

x-24 = 0     => x=24

As length cannot be 0 therefore,

Longer leg = x = 24 feet

Shorter leg = x-6 = 24-6 = 18 feet

Hypotenuse = x+6 = 24+6 = 30 feet.

The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.

Keywords: triangle, addition

Learn more about triangles at:

#LearnwithBrainly

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