The area of a rectangle is 48 square centimeters.

Ответ:

tayjohnson0042

11.01.2022

The dimensions of the original rectangle are 8 cm x 6 cm

Step-by-step explanation:

Let

x----> the length of the original rectangle

y----> the width of the original rectangle

we know that

The area of the original rectangle is

A=xy

$A=48\ cm^{2}$

48=xy

x=48/y -----> equation A

If the length and width are each increased by 4 centimeters, the area of the larger rectangle is 120 square centimeters

$120=(x+4)(y+4)\\120=xy+4x+4y+16$

xy+4x+4y-104=0 -----> equation B

Substitute equation A in equation B

48+4(48/y)+4y-104=0

Multiply by y both sides

$48y+192+4y^{2}-104y=0\\ \\4y^{2}-56y+192=0$

using a graphing tool------> solve the quadratic equation

I assume that the length is greater than the width

The solution is $y=6\ cm$

see the attached figure

Find the value of x

$x=48/6=8\ cm$

The dimensions of the original rectangle are 8 cm x 6 cm

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