Question

Please help me I usually know how to do this but I idk what I am doing wrong

Answer 1

well,  we know the dimensions, width is "x" and lenght is "x+1"
area is A = l * w, so we know the area is 30

thus 30 = (x+1)x

$\bf 30=(x+1)x\implies 30=x^2+x\implies \begin{array}{lcclll} 0=x^2&+x&-30\\ &\uparrow &\uparrow \\ &6-5&6\cdot -5 \end{array} \\\\\\ 0=(x+6)(x-5)\implies x= \begin{cases} -6\\ 5 \end{cases}$

well, the width can't be -6, so it has to be 5

Answer 2

The area of this square is (x+1)(x+1) = (x+1)²

(x+1)²=x²+2x+1=30

Now solve the quadratic equation


x²+2x-29.

You will find 2 values of x, one is positive & the second is negative (to be ignored) & the x= -1+√30 or 4.477 cm