Question

The length of a rectangular picture frame is 3 inches shorter than its width. If the perimeter of the picture frame is 38 inches, what is the length, l, and width, w, of the frame? Write and solve an equation to model the problem. Explain the meaning of the solution.

Answer 1

${\frak{\underline{\blue{proper \: question: }}}}$

The length of a rectangular picture frame is 3 inches longer than it's width. If the perimeter of the picture frame is 38 Inches, what is the length and width ?

${\frak{\underline{\blue{solution: }}}}$

Given :

• Perimeter of rectangle is 38 Inches

• lenght is 3 inches more than the breadth.

${\bf{\underline{perimeter \: of \: rectangle \: = 2 \times( l + b)}}}$

let, width be x, and length be x+3

$\longrightarrow\sf \: 2 \times (l + b) = 38 \\ \\ \longrightarrow \sf \: 2(x + x + 3) = 38 \\ \\ \sf\longrightarrow \: 2x + 2x + 6 = 38 \\ \\ \sf\longrightarrow \: 4x + 6 = 38 \\ \\ \sf \longrightarrow \: 4x = 38 - 6 \\ \\ \sf\longrightarrow \: 4x = 32 \\ \\ \sf\longrightarrow \: x = \frac{32}{4} \\ \\ \bf\longrightarrow \: x = 8$

So, Breadth is 8 inches and length is 8+3= 11 inches.

Let's verify ::

$\sf = > 2 \times (l + b) = 38 \\ \\ = > \sf \: 2 \times( 11 + 8) = 38 \\ \\ \sf \: = > 2 \times 19 = 38 \\ \\ \sf = > 38 = 38$

$\bf \: LHS \: = \: RHS \:$

Thus Solved !!