Find the dimensions of a rectangle whose perimeter is 16 meters and whose area is 15 square meters.

2(x+y)=16,
x+y=16/2=8
y=8-x
x*y=15
x(8-x)=15
8x-x^2=15
x^2-8x+15=0
x^2-3x-5x+15=0
x(x-3)-5(x-3)=0
(x-3)(x-5)=0
x=3,5
when x=3
y=8-3=5
when x=5
y=8-5=3
length=5 meters
width=3 meters.

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abidemiokin abidemiokin · Answer 2 · 2022-06-22T06:16:09-04:00

The dimensions of a rectangle whose perimeter is 16 meters and whose area is 15 square meters is 3m by 5m

Area and perimeter of rectangle

The formula for calculating the area and perimeter of rectangle is expressed as:

A = lw

P = 2(l+w)

where l is the length and w is the width

Given the following

P = 16m

A = 15m²

Substitute

lw = 15 ............ 1

2(l + w) = 16

____________

lw = 15

l + w = 8 ................ 2

From equation 2, l = 8 - w

Substitute into 1

(8-w)w = 15

-w² + 8w = 15

w²- 8w + 15 = 0

Factorize

w² - 3w - 5w + 15 = 0

w(w-3)-5(w-3) = 0

w= 3m

Since lw = 15

l = 15/3

l = 5m

Hence the dimensions of a rectangle whose perimeter is 16 meters and whose area is 15 square meters is 3m by 5m

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