Question

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.

Answer 1

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

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