Chapter 11: Q26. (page 427)

The length of a rectangle is 12cmmore than its width. Find the area of the rectangle if its perimeter is 100cm.

Short Answer

Expert verified

The area of the rectangle is $589 c m^{2} .$

Step by step solution

Step 1. Given information.

Length of the rectangle $(h) 12 c m$ more than its width.

Perimeter of the rectangle $P = 100 c m$ .

Step 2. Concept Used.

If bis the base of the reactangle and h is the length 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 & perimeter of the rectangle.

Let $(x)$ be the width,

Then,

The length of the rectangle is 12cm more than its width.

i.e.

$l e n g t h (h) = x + 12$

Put the value of length and perimeter into the formula and find the value of x .

Perimeter of the rectangle:

$\begin{matrix} P = 2 (b + h) \\ 100 = 2 (x + x + 12) \\ 100 = 2 (2 x + 12) \\ 50 = 2 x + 12 \\ 2 x = 50 - 12 \\ x = \frac{38}{2} \\ x = 19 \end{matrix}$

Now, put the value of x into the formula and find area of the rectangle-

$\begin{matrix} A = b h \\ = (x) (x + 12) \\ = (19) (19 + 12) \\ = (19) (31) \\ = 589 c m^{2} \end{matrix}$

Therefore, the area of the rectangle is $589 c m^{2} .$

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The length of a rectangle is 12cmmore than its width. Find the area of the rectangle if its perimeter is 100cm.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

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

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