Value of x. Hypotenuse is the square route of 20 and one leg is x-2 other leg is x

Question

asked Apr 8, 2020 161k views

1 Answer

Miggy · Answer 1 · 2020-04-15T08:59:07+0000

Answer:

Explanation:

The Pythagorean Theorem is:

a^2=b^2+c^2

Where the hypotenuse is "a" and "b" and "c" are the legs of the triangle.

Knowing that:

$a=√(20)\\b=x-2\\c=x$

Susbstitute values into the Pythagorean Theorem and solve for x:

(√(20))^2=(x-2)^2+x^2

Remember that the square a binomial is:

$(a\±b)^2=a^2\±2ab+b^2$

Then:

$20=x^2-2(x)(2)+2^2+x^2\\20=x^2-4x+4+x^2\\2x^2-4x-16=0$

Use the Quadratic formula:

$x=(-b\±√(b^2-4ac))/(2a)\\\\x=(-(-4)\±√((-4)^2-4(2)(-16)))/(2(2))$

$x_1=4\\x_2=-2$

Choose the positive value.

Then:

x=4