Respuesta :

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
aksnkj

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,

[tex]h=b-4[/tex]

Area of the triangle

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

[tex]A=\dfrac{1}{2} \times h\times b[/tex]

Putting the value of h in the above equation,

[tex]48=\dfrac{1}{2} \times (b-4)\times b[/tex]

[tex]48\times 2= (b-4)\times b[/tex]

[tex]96= b^2-4b[/tex]

[tex]b^2-4b-96=0[/tex]

[tex]b^2-12b+8b-96=0[/tex]

[tex]b(b-12)+8(b-12)=0[/tex]

[tex](b-12)(b+8)=0[/tex]

Equate both equations to zero, we get,

[tex]b=12,-8[/tex]

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

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