The base of a triangle is twelve more than twice its height. if the area of the triangle is 51 square centimeters, find its base and height.

The base and height of the triangle whose area is 51 and base of a triangle is twelve more than twice its height are 21.49 cm and 4.745 cm respectively.

Solution:

Given that  

The base of a triangle is twelve more than twice its height

And area of triangle = 51 square centimeter  

Let’s assume height of triangle = "x" cm

So base of triangle = 12 + (2 height ) = 2x + 12

On substituting the given value of area and assumed values of height and base in above formula we get

We can find solution of this equation using quadratic formula.

According to quadratic formula for general equation   solution of the equation is given by

Our equation is

So in our case, a = 1 , b = 6 and c = -51

On applying quadratic formula we get

As dimensions of triangle cannot be negative so neglect negative value

Height of triangle = x =  4.745 cm

Base of  triangle = 12 + ( 2 x 4.745  ) = 12 + 9.49 = 21.49 cm

Hence base and height of the triangle whose area is 51 and base of a triangle is twelve more than twice its height are 21.49 cm and 4.745 cm respectively.

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3