a right angled triangle has an area of 26cm^2

Question

the width of the triangle is n + 6cm the heigh is 9 cm less than the width find the value of n

also 4x^2 - 3x + 13 = 5x + 10

 

all help is much appreciated

Answer 1

Width=n+6, height=n+6-9=n-3. Area is (1/2)(n-3)(n+6)=26; n^2+3n-18=52; n^2+3n-70=0=(n+10)(n-7)=0, so n=7 or -10. so n+6 and n-3 are 13 and 4, because negative lengths, -4 and -13, can be rejected.

4x^2-3x+13=5x+10; 4x^2-8x+3=0=(2x-3)(2x-1), x=3/2 or 1/2.