Question

The height of a triangle is 2 yards greater than the base. The area of the triangle is 60 square yards.

Answer 1

base=10

height=12

Explanation:

Area of triangle formula is given by: A = (1/2)*b*h

where b: base of the triangle

h: height of the triangle

Given that: h=b+2

A= 60 square yards

Solution:

60= (1/2)*b*(b+2)

`(b(b+2))/(2)` = 60

b²+2b=120

b²+2b-120=0

We got the quadratic equation: b²+2b-120=0

solve it to find b:

Let x: coefficient of b² (x=1)

Let y: coefficient of b (y=2)

Let z: constant (z= -120)

discriminant= y² - 4xz = 4 - 4(1)(-120) = 484

discriminant>0 so the equation has two roots:

b1= (-y-redical discriminant)/2x = (-2-redical(484))/2 = -12

b2= (-y+redical discriminant)/2x = (-2+redical(484))/2 = 10

b1= -12 is rejected because the base can't be negative

So b2=base=10

Now that we found the base, substitute to get the height:

h= b+2 = 10+2 =12

So height=12

Answer 2

Explanation:

h=b+2(assume h is hieght and b is base)

b*(b+2)=60

bb+2b=60

b=-1+√61

h=1+√61