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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 11: Q11. (page 426)

The base of a rectangle is 16cmand perimeter is42cm. What is the area and height of the rectangle?

Short Answer

Expert verified

The area of the rectangle is $80 c m^{2}$ and height is5cm .

Step by step solution

01

Step 1. Given information.

Base of the rectangle $b = 16 c m$

Perimeter of the rectangle $P = 42 c m$ .

02

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

$P = 2 (b + h)$

03

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

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

Height of the rectangle :

$\begin{matrix} P = 2 (b + h) \\ 42 = 2 (16 + h) \\ 21 = 16 + h \\ h = 21 - 16 \\ h = 5 c m \end{matrix}$

Area of the rectangle:

$\begin{matrix} A = b \times h \\ = 16 \times 5 \\ = 80 c m^{2} \end{matrix}$

Therefore, the area of the rectangle is $80 c m^{2}$ and height is 5cm

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