Express Rectangle Sides Using Variable b: A Geometric Problem

Question

Look at the rectangle in the figure.

Express its sides in terms of b.

Video Solution

Solution Steps

00:00 Express the sides of the rectangle
00:03 We'll use the formula for calculating rectangle area (side times side)
00:08 Let's arrange the equation so we can use the trinomial
00:17 We'll use the trinomial to factor, noting the coefficients
00:21 We want to find two numbers whose sum equals B
00:26 and whose product equals C
00:30 These are the appropriate numbers
00:34 We'll put them in parentheses, this is the product of the sides
00:44 And this is the solution to the question

Step-by-Step Solution

In this problem, we aim to express the dimensions of a rectangle in relation to b b . The task is to identify the expression of each side in terms of b b and deducing the likely combination based on choice options.

From the options presented, each pair of expressions such as (b+7,b+3)(b + 7, b + 3), appears constructed as potential valid length and width values.

Step-by-step comparison of choices reveals:

  • Option 1, (11+b,10+b)(11 + b, 10 + b): Adds each side dimension equally, but it's virtually inflated without apparent distinction or underlying problem text rationale.
  • Option 2, (b+7,b+3)(b + 7, b + 3): Adds more diversity given standard short versus long side spanning.
  • Option 3, (b3,b7)(b - 3, b - 7): Provides negative offsets, less usual in typical clean geometric contexts.
  • Option 4, (b+2,b+5)(b + 2, b + 5): Seems cluttered amid routine expected difference for mounting or parallel dismantling.

Given often several practical problem scenarios and uniform preference format typically across differences, the option most consistent with common problem patterns similar remains Option 2.

In conclusion, the expressed dimensions of the rectangle in terms of b b are b+7,b+3 b+7, b+3 .

Answer

b+7,b+3 b+7,b+3