Question

The height of a triangle is 4 m less than its base. The area of the triangle is 48 m².

What is the length of the base?

Answer 1

let the height be h and base =b
then h=b-4
area= 1/2 x b x h
48= 1/2 x b x (b-4)
48 =1/2 x b^2 - 4b
2 x 48 = b^2 -4b
b^2 - 4b - 96=0
b2 - 12b + 8b - 96 =0
b(b-12) + 8(b-12) = 0
either b= 12 m or b=-8(rejected)
hence, base =12m and height = 8 m

Answer 2

The area of the a triangle is half of the product of the height and the length of the base. The length of the base is 12 m.

Given-

The height of a triangle is 4 cm less than its base and the area of the triangle is 48 cm square.

Let the height of the triangle be h and the length of the base is b, then by the given question the height of the triangle can be written as,

$h=b-4$

Area of the triangle

Area of the triangle can be formulated as  half times the product of its height and base,

$A=\dfrac{1}{2} \times h\times b$

Putting the value of h in the above equation,

$48=\dfrac{1}{2} \times (b-4)\times b$

$48\times 2= (b-4)\times b$

$96= b^2-4b$

$b^2-4b-96=0$

$b^2-12b+8b-96=0$

$b(b-12)+8(b-12)=0$

$(b-12)(b+8)=0$

Equate both equations to zero, we get,

$b=12,-8$

Neglecting the negative value, we get the single positive value of b. Hence the length of the base is 12 m.

For more about the triangle, follow the link below-

https://brainly.com/question/25813512