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Chapter 11: Q14. (page 426)

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

Short Answer

Expert verified

The area of the rectangle is(k2+10k+21) and height is(k+3) .

Step by step solution

01

Step 1. Given information.

Base of the rectangleb=(k+7)

Perimeter of the rectangleP=(4k+20) .

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 isA=b脳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 base and perimeter into the formula and find the height.

Height of the rectangle:

P=2(b+h)4k+20=2(k+7+h)4k+20=2k+14+2h2h=4k+20鈭�14鈭�2k2h=2k+6h=2(k+3)2h=(k+3)

Area of the rectangle :

A=b脳h=(k+7)脳(k+3)=(k2+7k+3k+21)=(k2+10k+21)

Therefore, the area of the rectangle is(k2+10k+21) and heigh is (k+3).

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