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MATH / A square has a side length of 10 inches. Congruent isosceles right triangles are…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A square has a side length of 10 inches. Congruent isosceles right triangles are cut off each corner so that the resulting octagon has equal side lengths. How many inches are in the length of one side of the octagon? Express your answer as a decimal to the nearest hundredth. [asy]
size(150);
draw((0,0)--(10,0)--(10,10)--(0,10)--(0,0),linewidth(0.7));
draw((5*sqrt(2)/(1 + sqrt(2)),0)--(0,5*sqrt(2)/(1 + sqrt(2))),linewidth(0.7));
draw((10 - (5*sqrt(2)/(1 + sqrt(2))),0)--(10,5*sqrt(2)/(1 + sqrt(2))),linewidth(0.7));
draw((0,(10-(5*sqrt(2)/(1+sqrt(2)))))--(5*sqrt(2)/(1 + sqrt(2)),10),linewidth(0.7));
draw((10 - (5*sqrt(2)/(1 + sqrt(2))),10)--(10,10 - 5*sqrt(2)/(1 + sqrt(2))),linewidth(0.7));
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
1ac6c774-5f83-5f8e-b33d-0be234e22431
task_key
geometry--test--1ac6c774-5f83-5f8e-b33d-0be234e22431
task_revision_id
1
config / split
geometry / test

Official source

initial import