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More Lessons for Algebra, Math Worksheets

How to solve geometry word problems that involve geometric figures and angles described in words? You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

### Geometry Word Problems Involving Area

The following video gives another example of geometry word problem that involves area.

Example: A rectangle is twice as long as it is wide. If the area of the rectangle is 98 cm^{2}, find its dimensions.
Writing quadratic equations to solve word problems: Area of a triangle

Example: The height of a triangles is 3 cm more than its base. The area of the triangle is 17 cm^{2}. Find the base to nearest hundredth of a cm.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Algebra, Math Worksheets

How to solve geometry word problems that involve geometric figures and angles described in words? You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

Example:

A rectangle is 4 times as long as it is wide. If the length is increased by 4 inches and the width is decreased by 1 inch, the area will be 60 square inches. What were the dimensions of the original rectangle?

Solution:

Step 1: Assign variables:

Letx= original width of rectangle

Sketch the figure

Step 2: Write out the formula for area of rectangle.

A =lw

Step 3: Plug in the values from the question and from the sketch.

60 = (4

x+ 4)(x–1)Use distributive property to remove brackets

60 = 4x^{2}– 4x+ 4x– 4Put in Quadratic Form

4x^{2}– 4 – 60 = 0

4x^{2}– 64 = 0This quadratic can be rewritten as a difference of two squares

(2x)^{2}– (8)^{2}= 0Factorize difference of two squares

(2x)^{2}– (8)^{2}= 0

(2x– 8)(2x+ 8) = 0We get two values for

x.

Since

xis a dimension, it would be positive. So, we takex= 4The question requires the dimensions of the original rectangle.

The width of the original rectangle is 4.

The length is 4 times the width = 4 × 4 = 16

Answer: The dimensions of the original rectangle are 4 and 16.

Example: A rectangle is twice as long as it is wide. If the area of the rectangle is 98 cm

Example: The height of a triangles is 3 cm more than its base. The area of the triangle is 17 cm

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You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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