Chapter 10: Q15. (page 603)

The area of the rectangle is 90 square feet. Find $x$ .

Short Answer

Expert verified

The values of $x = - 9, 10$ .

Step by step solution

Step 1. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equal sign $" = "$ .

Step 2. Write the standard form of a quadratic equation.

The standard form of a quadratic equation is given by

$a x^{2} + b x + c = 0$ , where $a \neq 0$

Step 3. Define the area of the rectangle.

$Area of the rectangle = length \times width \dots \dots \dots . . (1)$

Step 4. Find the value of x for the given rectangle.

Observe the figure.

The length of the rectangle $= (x - 1)$ feet

The width of the rectangle $= x$ feet

The area of the rectangle $= 90$ square feet

Use equation (1).

role="math" localid="1647949732123" $(x - 1) (x) = 90 x^{2} - x = 90 x^{2} - x - 90 = 0 x^{2} - 10 x + 9 x - 90 = 0 x (x - 10) + 9 (x - 10) = 0 (x - 10) (x + 9) = 0 x = - 9, 10$

Therefore the values of $x = - 9, 10$ .

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The area of the rectangle is 90 square feet. Find $x$ .

Short Answer

Step by step solution

Step 1. Define an equation.

Step 2. Write the standard form of a quadratic equation.

Step 3. Define the area of the rectangle.

Step 4. Find the value of x for the given rectangle.

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The area of the rectangle is 90 square feet. Find x.

Short Answer

Step by step solution

Step 1. Define an equation.

Step 2. Write the standard form of a quadratic equation.

Step 3. Define the area of the rectangle.

Step 4. Find the value of x for the given rectangle.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Decision Maths

Calculus

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

The area of the rectangle is 90 square feet. Find $x$ .