Question

the length of a triangle is 3 centimeters less than twice its width its area is 35 square centimeters find the dimensions of the rectangle use formula area=length*width the width is ?_ the Length is?_

Answer 1

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We have:

• The length of a triangle is 3 centimeters less than twice its width.
• Area = 35 cm²

We need to find:

• Dimensions of the rectangle?

Solution:

Let the width be w. Then the length would be:

➝ Length = 2(width) - 3

➝ l = 2w - 3

Area of rectangle: l × b

➝ Length × width = 35 cm²

➝ (2w - 3)w = 35

➝ 2w² - 3w - 35 = 0

Now finding value of x by middle term factorisation,

➝ 2w² - 10w + 7w - 35 = 0

➝ 2w(w - 5) + 7(w - 5) = 0

➝ (2w + 7)(w - 5) = 0

Hence,

• w = 5 because width can't be negative.
• l = 2(5) - 3 = 7

Therefore,

• Width = 5 cm
• Length = 7 cm

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Answer 2

let x represent the rectangle's width;

thus;

Width = x

Length = 2x - 3

Area = 35 sq. cm.

Area = Length × Width

35 = (2x - 3)(x)

35 = 2x^2 - 3x

2x^2 - 3x - 35 = 0

Factorizing:

x = 5 or -3.5

but width is a scalar quantity and cannot be negative:

Hence:

Width = 5 cm.

Length = 2(5) - 3 = 7 cm.

6x = 41

x = 7 to the nearest whole number.

Width = 7 cm.

Length = 2(7) - 3 = 11 cm.