Question

the height of right angle triangle is 3 cm less than twice its base. The area of the triangle is 7 cm square .Write a quadratic equation in X in the standard form.​

Answer 1

Step-by-step explanation:

(By pythagoras theorem)

⟹(x−7) 2+x 2 =13

2

⟹x 2 +x 2+49−14x=169

⟹2x 2−14x+(49−169)=0

⟹2x 2 −14x−120=0

⟹x 2 −7x− 2- 120 =0

⟹x 2 −7x−60=0

⟹x 2 −12x+5x−60=0

⟹x(x−12)+5(x−12)=0

⟹(x−12)(x+5)=0

∴x=12 (x=-5 is not possible since side can't be negative)

∴Base=12cm

Answer 2

Answer:

let the height be = x

let the base be = 2x - 3

we know area = ½BH

= [x (2x-3)/2]

given area = 7cm²

therefore the equation would be like

=> x(2x-3)/2 = 7

=> 2x² - 3x -14 = 0

hope it helped :)