benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / As shown, a square is constructed on the hypotenuse of a right triangle whose…

Problem

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

problem

As shown, a square is constructed on the hypotenuse of a right triangle whose legs have lengths 3 units and 4 units. What is the area of the pentagon ABCDEABCDE, in square units? [asy] pair a,b,c,d,e; a=(3,7); b=(7,4); c=(4,0); d=(0,0); e=(0,3); draw((0,0.5)--(0.5,0.5)--(0.5,0)); label("4",(2,0),S); draw(a--b--c--e--d--c--e--a); label("3",(0,1.5),W); label("AA",a,N); label("BB",b,E); label("CC",c,S); label("DD",d,S); label("EE",e,W); [/asy]
Plain-text mathematical notation (without MathML)
As shown, a square is constructed on the hypotenuse of a right triangle whose legs have lengths 3 units and 4 units. What is the area of the pentagon ABCDE, in square units?

[asy]
pair a,b,c,d,e;
a=(3,7);
b=(7,4);
c=(4,0);
d=(0,0);
e=(0,3);
draw((0,0.5)--(0.5,0.5)--(0.5,0));
label("4",(2,0),S);
draw(a--b--c--e--d--c--e--a);
label("3",(0,1.5),W);
label("A",a,N);
label("B",b,E);
label("C",c,S);
label("D",d,S);
label("E",e,W);
[/asy]
Original LaTeX notation
As shown, a square is constructed on the hypotenuse of a right triangle whose legs have lengths 3 units and 4 units. What is the area of the pentagon $ABCDE$, in square units?

[asy]
pair a,b,c,d,e;
a=(3,7);
b=(7,4);
c=(4,0);
d=(0,0);
e=(0,3);
draw((0,0.5)--(0.5,0.5)--(0.5,0));
label("4",(2,0),S);
draw(a--b--c--e--d--c--e--a);
label("3",(0,1.5),W);
label("$A$",a,N);
label("$B$",b,E);
label("$C$",c,S);
label("$D$",d,S);
label("$E$",e,W);
[/asy]

level

Level 3

type

Prealgebra

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
ec4f2ac0-406f-5a1e-87b0-e74dcb0abb4d
task_key
prealgebra--test--ec4f2ac0-406f-5a1e-87b0-e74dcb0abb4d
task_revision_id
1
config / split
prealgebra / test

Official source

initial import