Question

A triangular banner has an area of 351 cm squared. The length of the base is two centimeters longer than four times the height. Find the length and height of the base

Answer 1

Answer:

Let height be x cm

Then, Base = (4x + 2 )

Area of Triangle = 351 cm²

1/2 base × height= 351 cm²

1/2 (4x+2)x = 351

(2x + 1)x = 351

2x²+x-351 = 0

2x²+(27-26)x - 351 = 0

2x²+27x -26x -351=0

2x²-26x +27x-351=0

2x(x-13) +27(x-13)=0

(x-13) (2x+27)= 0

i.e., either

x-13=0 or 2x+27=0

x=13 or x = -27/2

Taking x = 13,

Height =13 cm

Base = 4×13+2

= 52+2

= 54cm