Question

the height of a triangle is 4cm less than twice the length of its base, and the area is 15cm squared. find the length of the triangles base

Answer 1

length of the base = 5cm , height = 6cm

Explanation:

Let the length of it's base be x , since the height of a triangle is 4cm less than twice the length of its base,

twice it's base = 2x

Therefore , the height = 2x - 4

Area = 15
`cm^(2)`

The formula for finding the area of a rectangle is given as :

Area =
`(1)/(2)` x base x height

Therefore:

15 =
`(1)/(2)` x
`x` x
`2x - 4`

`15 = x^(2) - 2x`

therefore :

`x^(2) -2x-15 = 0`

factorizing , we have

`(x-5)(x+3) = 0`

which means that

`x = 5` or
`-3`

since the length of the base can not be negative , then , the length of the base is 5 cm

height = 2(5) - 4

height = 10 - 4

height = 6