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A rhombus is inscribed in a rectangle that is w meters wide with a perimeter of 56 m. Each vertex of the rhombus is a midpoint of a side of the rectangle. Express the area of the rhombus as a function of the rectangle's width

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5naka

let the rectangle l meters long

perimeter = 2l + 2w

56 = 2l + 2w

28 = l + w

l = 28 - w

area of rhombus = ½•l•w

f(w) = ½•(28-w)•w

= 14w - ½w²

ashishdwivedilVT

The area of the rhombus as a function of the rectangle's width is f(y) = 14y - ½y².

What is Rhombus?

A rhombus is a quadrilateral whose four sides all have the same length.

Here,

Let the length of rectangle be x meters

Perimeter of rectangle = 56 meters.

perimeter = 2(x+y)

56 = 2(x+y)

28 = x+y

x = 28 - y

area of rhombus = ½•x•y

f(y) = ½•(28-y)•y

f(y) = 14y - ½y²

Thus, the area of the rhombus as a function of the rectangle's width is f(y) = 14y - ½y².

Learn more about Rhombus from:

https://brainly.com/question/22825947

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