The base of a triangle exceeds the height by 9 centimeters. If the area is 56 square centimeters, find the length of the base and the height of the triangle.

The height of the triangle is 7cm and the base is 16cm

Step-by-step explanation:

First of all we have to know the formula to calculate area of a triangle

a = area = 56

b = base

h = heigth

a = (b * h)/2

we replace the known values and we make 2 equations

56cm² = (b * h)/2

b = h + 9cm

we replace b by (h + 9cm) in the first equation

56cm² = (h + 9cm * h)/2

56cm² * 2 = h² + 9h

0 = h² + 9h - 112cm²

we use bhaskara formula:

(-b (±) √ (b² - 4ac) ) / 2a

we replace with the known values

h = (-9 (±) √ (9² - 4*1*(-112) ) ) / 2*1

h = (-9 (±) √ (81 + 448) ) ) / 2

h = (-9 (±) √529) /2

h = (-9 (±) 23)/2

h1 = (-9 + 23) / 2

h1 = 14 / 2

h1 = 7

h2 = (-9 - 23) / 2

h2 = -32 / 2

h2 = -16

The height of the triangle is 7cm and the base is 16cm

answer:

the position of equilibrium will shift to the left.

step-by-step explanation:

the general equation for the dissociation of a weak base is

b + h₂o   ⇌   bh⁺ + oh⁻

according to le châtelier's principle, when a stress is applied to a system at equilibrium, the system will respond in a way that tends to relieve the stress.

if you apply a stress by adding more bh⁺ or oh⁻,   the system will respond by moving in a direction that gets rid of the added ions.

the position of equilibrium will shift to the left, forming more of the undissociated base.