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The length of a rectangle is 7 centimeters less than three times its width. Its area is 40 square centimeters. Find the dimensions of the rectangle.

Sagot :

If the area of the rectangle is 40 square centimeters and length is 7 cm less than 3 times the breadth then the length will be 8 cm and breadth will be 5 cm.

Given area of the rectangle is 40 square centimeters and length is 7 centimeters less than 3 times the breadth.

let the breadth of rectangle be x.

According to question

Length=3x-7

Breadth=x

Area of  rectangle=length* breadth

=[tex](3x-7)x[/tex]

=[tex]3x^{2} -7x[/tex]

Area is given as 40 square centimeters.

40=[tex]3x^{2} -7x[/tex]

[tex]3x^{2} -7x-40=0[/tex]

By factorization

[tex]3x^{2} -15x+8x-40=0[/tex]

3x(x-5)+8(x-5)=0

(3x+8)(x-5)=0

3x+8=0

x=-8/3

x-5=0

x=5

We should neglect x=-8/3 because side cannot be negative. So we have taken x=5.

Put x=5 in 3x-7 to get length

length=3(5)-7

=15-7

=8

Hence the length will be 8 cm and breadth will be 5 cm.

Learn more about area at https://brainly.com/question/25965491

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