WORD PROBLEMS ON POLYNOMIALS INVOLVING AREA AND PERIMETER

Express the area of the figure as a polynomial in descending powers of the variable x.

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Problem 3 :

The area of a rectangle is 20m² – 13m – 15. Find the length if the width is 4m – 5.

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Problem 4 :

A rectangular patio has an area of 2m³ + 12m² + 6m – 40. Find the length if the width is 2m + 8.

Solution

Find simplified expressions for the perimeter and area of the given figure.

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Problem 7 :

The area of a rectangular window is (2x² – 7x – 15). Both the length and the width are polynomials with integer coefficients. Which of the following could represent the length of the window?              Solution

Problem 8 :

A triangle is inscribed in a square, as shown. Write and simplify a function r in terms of x that represents the area of the shaded region.

Solution

Find the length of missing side.

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Problem 4 :

The measure of the perimeter of a triangle is 37s + 42. It is known that two of the sides of the triangle have measures of 14s + 16 and 10s + 20. Find the length of the third side.            Solution

Problem 5 :

A triangle has a perimeter of 10a + 3b + 12 and has sides of length 3a + 8 and 5a + b, what is the length of the third side?               Solution

Problem 6 :

For a rectangle with length of 3x + 4 and perimeter of 10x + 18, what is the width of the rectangle?           Solution

Problem 7 :

A rectangle has a perimeter of 12y² - 2y + 18 and has a width of 4y² - y + 6. What is the length of the rectangle?   

Solution

Find the perimeter of the shapes given below.

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Problem 9 :

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