Question

I need help with 25.

Answer 1

so the area A is no more than 10, namely A ⩽ 10 , it could be 10 or less, but no more than that.

let's recall the area of a triangle is A = (1/2)bh

`\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=4\\ h=2x-3 \end{cases}\implies A=\cfrac{1}{2}(4)(2x-3) \\\\[-0.35em] ~\dotfill\\\\ A\leqslant 10\implies \cfrac{1}{2}(4)(2x-3)\leqslant 10\implies 2(2x-3)\leqslant 10\implies 4x-6\leqslant 10 \\\\\\ 4x\leqslant 16\implies x\leqslant \cfrac{16}{4}\implies x\leqslant 4 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{maximum height of the triangle}}{2(4)-3}\implies 8-3\implies 5`

when x = 4 is the maximum height, since x ⩽ 4, so it could be 4 at most, could be less than 4 or equals but never higher.