Quadratic equations

Question

A triangular banner has an area of 351cm. The length of the base is 2 centimeters longer than 4 times the height. Find height and length of the base

Answer 1

Let h=height

Let 4h+2 = base

Area of a triangle = 1/2bh

351=1/2(h)(4h+2)

Multiply both sides by 2 to clear the fraction and simplify.

351*2=1/2(h)(4h+2)*2

702=h(4h+2)

Distribute the h

702=4h²+2h

Subtract 702 from both sides and simplify

702-702=4h²+2h-702

0=4h²+2h-702

Divide both sides by 2 and simplify

0/2=4h²/2+2h/2-702/2

0=2h²+h-351

This can be solved by factoring

0=(2h+27)(h-13)

2h+27=0 and h-13=0

h=-13.5 (non a valid dimension, cannot be negative) and h=13 cm is the height

4h+2 = 4(13)+2 = 54 cm for the base