Question

The altitude of a right triangle is 4cm greater than its
base. If its area is 96cm², find the base & height of the
triangle


(chapter quadratic equation)


please explain the answer ​

Answer 1

Answer:

the base will be = 12 cm and height =16cm

Step-by-step explanation:

let the base be = x

so, the altitude will be = 4+x

area of a triangle=

$\frac{1}{2}*b*h\\\\\frac{1}{2}*x*(x+4)= 96\\\\{x}^{2}+ 4x =192\\\\{x}^{2}+ 4x -192 = 0\\\\{x}^{2}+ 16x - 12 x - 192 =0\\\\x(x+16)-12(x + 16)=0\\\\(x-12)(x+16)=0\\\\x = 12 \:\: or -16$

side can't be negative so the base is 12 cm and the altitude is 16 cm.

⇒Hope this helps you!