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MATH / The measure of one of the smaller base angles of an isosceles trapezoid is…

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

problem

The measure of one of the smaller base angles of an isosceles trapezoid is 60∘60^\circ. The shorter base is 5 inches long and the altitude is 232 \sqrt{3} inches long. What is the number of inches in the perimeter of the trapezoid? [asy] import markers; import olympiad; size(150); import geometry; import graph; defaultpen(linewidth(0.8)); draw(origin--(9,0)--(7,2*sqrt(3))--(2,2*sqrt(3))--cycle); draw(Label("232\sqrt{3}",align=E),(2,2*sqrt(3))--(2,0),dashed); label("5",(7,2*sqrt(3))--(2,2*sqrt(3)),N); markangle(Label("60∘60^{\circ}"),(9,0),origin,(2,2*sqrt(3)),radius=10); [/asy]
Plain-text mathematical notation (without MathML)
The measure of one of the smaller base angles of an isosceles trapezoid is 60^(∘). The shorter base is 5 inches long and the altitude is 2√(3) inches long. What is the number of inches in the perimeter of the trapezoid? [asy]
import markers;
import olympiad; size(150); import geometry; import graph; defaultpen(linewidth(0.8));
draw(origin--(9,0)--(7,2*sqrt(3))--(2,2*sqrt(3))--cycle);
draw(Label("2√(3)",align=E),(2,2*sqrt(3))--(2,0),dashed);
label("5",(7,2*sqrt(3))--(2,2*sqrt(3)),N);
markangle(Label("60^(∘)"),(9,0),origin,(2,2*sqrt(3)),radius=10);
[/asy]
Original LaTeX notation
The measure of one of the smaller base angles of an isosceles trapezoid is $60^\circ$. The shorter base is 5 inches long and the altitude is $2 \sqrt{3}$ inches long. What is the number of inches in the perimeter of the trapezoid? [asy]
import markers;
import olympiad; size(150); import geometry; import graph; defaultpen(linewidth(0.8));
draw(origin--(9,0)--(7,2*sqrt(3))--(2,2*sqrt(3))--cycle);
draw(Label("$2\sqrt{3}$",align=E),(2,2*sqrt(3))--(2,0),dashed);
label("5",(7,2*sqrt(3))--(2,2*sqrt(3)),N);
markangle(Label("$60^{\circ}$"),(9,0),origin,(2,2*sqrt(3)),radius=10);
[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
a1a7b626-d2a6-5a7e-a2af-1d57fc97f51e
task_key
geometry--test--a1a7b626-d2a6-5a7e-a2af-1d57fc97f51e
task_revision_id
1
config / split
geometry / test

Official source

initial import