a box is to be constructed with a rectangular base and a height of 5 cm. if the rectangular base must have a…

a box is to be constructed with a rectangular base and a height of 5 cm. if the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box?\n$v = lwh$\n$p = 2(l + w)$\n$y = 5(28 - x)(x)$\n$y = 5(28 - 2x)(x)$\n$y = 5(14 - x)(x)$\n$y = 5(14 - 2x)(x)$

a box is to be constructed with a rectangular base and a height of 5 cm. if the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box?\n$v = lwh$\n$p = 2(l + w)$\n$y = 5(28 - x)(x)$\n$y = 5(28 - 2x)(x)$\n$y = 5(14 - x)(x)$\n$y = 5(14 - 2x)(x)$

Answer

Explanation:

Step1: Express length in terms of width

Given perimeter formula $P = 2(l + w)$ and $P=28$ cm. So, $28 = 2(l + w)$, then $l + w=14$, and $l = 14 - w$. Let $w = x$.

Step2: Calculate volume

Volume formula is $V=lwh$. Given $h = 5$ cm, $l=14 - x$, $w = x$. Substitute into volume formula: $V=5(14 - x)(x)$. Let $y = V$. So the quadratic - equation is $y = 5(14 - x)(x)$.

Answer:

$y = 5(14 - x)(x)$