Question

The height of a triangle is 5 m less than its base. The area of the triangle is 42 m². What is the length of the base? Enter your answer in the box.

Answer 1

Area of a triangle=1/2bh
h=b-5
42=1/2*b*(b-5)
42=1/2*b^2-5b
84=b^2-5b
b^2-5b-84=0
b^2+7b-12b-84=0
b(b+7)-12(b+7)=0
b=12,b=-7

so width cant be negative so base =12 m
H=12-5=7 m

Answer 2

The length of the base is 12 m

Explanation:

Given : The height of a triangle is 5 m less than its base. The area of the triangle is 42 m².

We have to find the length of the base.

Given the height of triangle is 5 m less than base

Let base be x then height is ( x -5 ) m

Area of triangle is
`(1)/(2) * base * height`

also given area of triangle is 42 m²

substitute, we get,

`42=(1)/(2) * x * (x-5)`

Solving , we get,

`84=x(x-5)`

Simplify we get a quadratic equation as,

`x^2-5x-84=0`

Using quadratic formula,

For the standard quadratic equation
`ax^2+bx+c=0` , the solution of roots is given by,
`x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)`

For a = 1 , b= -5 , c = -84 , we get

`x_(1,\:2)=(-\left(-5\right)\pm √(\left(-5\right)^2-4\cdot \:1\left(-84\right)))/(2\cdot \:1)`

Simplify, we get

`=(5\pm√(361))/(2\cdot \:1)`

We know
`√(361)=19` , we get

`x_(1,2)=(5\pm19)/(2)`

`x_1=(5+19)/(2)` and
`x_2=(5-19)/(2)`

`x_1=12` and
`x_2=-7`

ignoring negative value as side cannot be negative.

thus, x = 12

base is 12 m then height is ( 12 -5 ) m = 4 m

Thus, the length of the base is 12 m.