Right triangle question

Question

A right triangle has a height 8 cm more than twice the length of the base. If the area of the triangle is 96 cm², what are the dimensions of the triangle. (6 marks)

Please answer in full detail

Answer 1

Area = hb/2 = (8+2b)b/2 = 96

(4+b)b = 96

4b+b^2 =96

b^2 + 4b - 96 = 0

factor

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

b= 8 or

use the quadratic formula

b =-4/2 +(1/2)sqr(16+4(96)

b=-2 + 10

b= 8 centmeters base

h=8+2(8) = 24 centimeters high

Area = 24(8)/2 = 96 cm^2

Answer 2

Area of a right triangle is half product of t wo legs. A=ab/2

are given b=2a +8 and A=96. Then you have a quadratic equation (2a² +8a)/2=96 or after simplifying a² +4a-96=0 use factoring (a-8)(a+12) = 0 that gives a=8 and as b cannot be negative b=2*8+8=24; check the solution 24*8/2=96