Chapter 11: Q14. (page 426)

The base of a rectangle is $(k + 7)$ and perimeter $(4 k + 20)$ . What is the area and height of the rectangle?

Short Answer

Expert verified

The area of the rectangle is $(k^{2} + 10 k + 21)$ and height is $(k + 3)$ .

Step by step solution

Step 1. Given information.

Base of the rectangle $b = (k + 7)$

Perimeter of the rectangle $P = (4 k + 20)$ .

Step 2. Concept Used.

If b is the base of the reactangle and h is the height of the rectangle.

Then, the area of the rectangle is $A = b \times h$

Perimeter of the rectangle is

$P = 2 (b + h)$

Step 3. Let’s calculate the area & height of the rectangle.

Put the value of base and perimeter into the formula and find the height.

Height of the rectangle:

$\begin{matrix} P = 2 (b + h) \\ 4 k + 20 = 2 (k + 7 + h) \\ 4 k + 20 = 2 k + 14 + 2 h \\ 2 h = 4 k + 20 - 14 - 2 k \\ 2 h = 2 k + 6 \\ h = \frac{2 (k + 3)}{2} \\ h = (k + 3) \end{matrix}$

Area of the rectangle :

$\begin{matrix} A = b \times h \\ = (k + 7) \times (k + 3) \\ = (k^{2} + 7 k + 3 k + 21) \\ = (k^{2} + 10 k + 21) \end{matrix}$

Therefore, the area of the rectangle is $(k^{2} + 10 k + 21)$ and heigh is $(k + 3)$ .

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The base of a rectangle is $(k + 7)$ and perimeter $(4 k + 20)$ . What is the area and height of the rectangle?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Let’s calculate the area & height of the rectangle.

One App. One Place for Learning.

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The base of a rectangle is(k+7)and perimeter(4k+20). What is the area and height of the rectangle?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Let’s calculate the area & height of the rectangle.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Mechanics Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

The base of a rectangle is $(k + 7)$ and perimeter $(4 k + 20)$ . What is the area and height of the rectangle?