How to find the pythagorean theorem?

x = 3*sqrt(15) = 11.61895

Step-by-step explanation:

Properties of the Triangle.

The triangle is isosceles                       It has 2 equal sides (24)

x meets the base at a right angle        Given

An altitude also is a median                 Property of Isosceles triangle

A median divides a base into 2 equal segments     Isoceles triangle

42 /2 = 21                                               Above Property

Find x

Formula

a^2 + b^2 = c^2

Givens

a = x

b = 21

c = 24

Solution

a^2 + b^2 = c^2          Substitute for a,b and c

x^2 + 21^2 = 24^2      

x^2 + 441 = 576          Subtract 441 from both sides.

x^2 = 576 - 441

x^2 = 135

135: 3*3*3*5

Take the square root of both sides

x = sqrt(135)

sqrt(135) = sqrt(3 * 3 * 3 * 5). For every pair of primes, you can take out 1 prime and throw the other one away. You are left with something under the root sign.

x = 3 * sqrt(15)    Answer

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.