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MATH / A picture frame consists of two rectangular strips of wood, each having a width…

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problem

A picture frame consists of two rectangular strips of wood, each having a width of 1 inch on all sides. If the area of the inner light gray strip is 100 in2\text{in}^2, then compute the area of the outer dark gray strip in square inches. [asy] import olympiad; import geometry; size(100); defaultpen(linewidth(0.8)); real width = 0.4; filldraw((origin)--(7,0)--(7,5)--(0,5)--cycle,fillpen=gray(0.2)); filldraw((origin + (width,width))--((7,0)+(-width,width))--((7,5)+(-width,-width))--((0,5)+(width,-width))--cycle,fillpen=gray(0.5)); filldraw((origin + 2(width,width))--((7,0)+2(-width,width))--((7,5)+2(-width,-width))--((0,5)+2(width,-width))--cycle,fillpen=white); [/asy]
Plain-text mathematical notation (without MathML)
A picture frame consists of two rectangular strips of wood, each having a width of 1 inch on all sides.  If the area of the inner light gray strip is 100 in², then compute the area of the outer dark gray strip in square inches. [asy]
import olympiad; import geometry; size(100); defaultpen(linewidth(0.8));
real width = 0.4;
filldraw((origin)--(7,0)--(7,5)--(0,5)--cycle,fillpen=gray(0.2));
filldraw((origin + (width,width))--((7,0)+(-width,width))--((7,5)+(-width,-width))--((0,5)+(width,-width))--cycle,fillpen=gray(0.5));
filldraw((origin + 2(width,width))--((7,0)+2(-width,width))--((7,5)+2(-width,-width))--((0,5)+2(width,-width))--cycle,fillpen=white);
[/asy]
Original LaTeX notation
A picture frame consists of two rectangular strips of wood, each having a width of 1 inch on all sides.  If the area of the inner light gray strip is 100 $\text{in}^2$, then compute the area of the outer dark gray strip in square inches. [asy]
import olympiad; import geometry; size(100); defaultpen(linewidth(0.8));
real width = 0.4;
filldraw((origin)--(7,0)--(7,5)--(0,5)--cycle,fillpen=gray(0.2));
filldraw((origin + (width,width))--((7,0)+(-width,width))--((7,5)+(-width,-width))--((0,5)+(width,-width))--cycle,fillpen=gray(0.5));
filldraw((origin + 2(width,width))--((7,0)+2(-width,width))--((7,5)+2(-width,-width))--((0,5)+2(width,-width))--cycle,fillpen=white);
[/asy]

level

Level 5

type

Prealgebra

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Source and history

task_id
b599dc00-3917-5bb5-a429-e042c3818224
task_key
prealgebra--test--b599dc00-3917-5bb5-a429-e042c3818224
task_revision_id
1
config / split
prealgebra / test

Official source

initial import