Question

The area of a triangle is 18 cm² and the sum of its base and altitude is 12 cm. Find the base and altitude.

Answer 1

Let the base be b cm and the altitude be h cm.

`"Area" = 1/2 xx b xx h`

Given area = 18 cm²:

`1/2 bh = 18`

bh = 36     ...(1)

b + h = 12     ...(2)

h = 12 − b

b(12 − b) = 36

12b − b² = 36

b² − 12b + 36 = 0

(b − 6)² = 0

b = 6

h = 12 − 6

= 6

The base and altitude of the triangle are:

6 cm and 6 cm​