Question

Searches related to The height of a triangle is 4 feet greater than the base. The area of the triangle is 336 square feet. Find the length of the base and the height of the triangle.

Answer 1

base = 24 ft

height = 28 ft

Explanation:

first we have to identify the 2 equations that give us

h = b+4

h*b/2 = 336

Now let's replace the h with (b + 4)

(b+4)*b/2 = 336

(b^2+4b)/2 = 336

b^2 + 4b = 336*2

b^2 + 4b = 672

b^2 + 4b - 672 = 0

when we have an equation of the form Ax ^ 2 + Bx + C = 0

we can use bhaskara

(-B√(B^2-4AC))/2A

we replace with the values

(-4√(4^2-4*1*-672))/2*1

b1 = -4 + 52 /2 = 24

b2 = -4 - 52 /2 = -28

we can only use positive values

b = 24

to know the height we replace b with 24 in the equation of the beginning

h = b+4

h = 24+4

h = 28

to corroborate we can calculate the area and see if it gives us correct

h*b/2 = 336

28*24/2 = 336

672/2 = 336

336 = 336

correct