Question

The perimeter of a rectangle is 42 cm. The width is 7 cm less than the length.

Answer 1

Answer:

Length = 14

Width =7

Step-by-step explanation:

$Let \:the\:length\:be \:x\\Perimeter = 42 cm\\Width = x -7\\\\P = 2(l+b)\\\\42 = 2(x+(x-7))\\\\42 = 2(x +x-7)\\42 = 2(2x-7)\\42 = 4x -14\\Collect\:like\:terms\\\\42+14=4x\\56 = 4x\\\\Divide \:both\:sides\:of\:the\:equation\:by \:4\\\frac{56}{4} = \frac{4x}{4} \\\\14 =x\\Length = 14\\Width = x-7\\Width = 14-7\\\\Width = 7$

Answer 2

Answer: length = 14cm width= 7cm, Area = 98cm^2

Explanation:

First let’s find the semi perimeter of the rectangle:

Semi. = P/2
Semi. = 42/2
Semi. = 21

Find length:

L + L - 7 = 21 (L - 7 is the width)
2L - 7 = 21
2L = 28
L = 28/2
L = 14

Find width:

Width is L - 7

But L is 14

W = 14 - 7
W = 7

Find area:

A = LW
A = 14 x 7
A = 98cm^2