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MATH / In the diagram below, △ABC is isosceles and its area is 240. What is the y-coordinate of A? [asy] import olympiad; // Draw and label axes draw((0, -3)--(0, 30), Arrow); draw((-3, 0…

Problem

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problem

In the diagram below, △ABC\triangle ABC is isosceles and its area is 240. What is the yy-coordinate of $A?$ [asy] import olympiad; // Draw and label axes draw((0, -3)--(0, 30), Arrow); draw((-3, 0)--(30, 0), Arrow); label("yy", (0, 30), N); label("xx", (30, 0), E); // Draw triangle pair a = (10, 24); pair b = (0, 0); pair c = (20, 0); draw(a--b--c--cycle); dot(a); dot(b); dot(c); // Label points label("AA", a, N); label("B(0,0)B(0, 0)", b, NW); label("C(20,0)C(20, 0)", c, S); // Tick marks add(pathticks(a--b, s=45)); add(pathticks(a--c, s=45)); [/asy]
Plain-text mathematical notation (without MathML)
In the diagram below, △ABC is isosceles and its area is 240.  What is the y-coordinate of $A?$

[asy]

import olympiad;

// Draw and label axes

draw((0, -3)--(0, 30), Arrow);

draw((-3, 0)--(30, 0), Arrow);

label("y", (0, 30), N);

label("x", (30, 0), E);

// Draw triangle

pair a = (10, 24); pair b = (0, 0); pair c = (20, 0);

draw(a--b--c--cycle);

dot(a); dot(b); dot(c);

// Label points

label("A", a, N);

label("B(0,0)", b, NW);

label("C(20,0)", c, S);

// Tick marks

add(pathticks(a--b, s=45));

add(pathticks(a--c, s=45));

[/asy]
Original LaTeX notation
In the diagram below, $\triangle ABC$ is isosceles and its area is 240.  What is the $y$-coordinate of $A?$

[asy]

import olympiad;

// Draw and label axes

draw((0, -3)--(0, 30), Arrow);

draw((-3, 0)--(30, 0), Arrow);

label("$y$", (0, 30), N);

label("$x$", (30, 0), E);

// Draw triangle

pair a = (10, 24); pair b = (0, 0); pair c = (20, 0);

draw(a--b--c--cycle);

dot(a); dot(b); dot(c);

// Label points

label("$A$", a, N);

label("$B(0, 0)$", b, NW);

label("$C(20, 0)$", c, S);

// Tick marks

add(pathticks(a--b, s=45));

add(pathticks(a--c, s=45));

[/asy]

level

Level 2

type

Geometry

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Source and history

task_id
3243d5d0-23ed-5f74-9793-423d36b80c53
task_key
geometry--test--3243d5d0-23ed-5f74-9793-423d36b80c53
task_revision_id
1
config / split
geometry / test

Official source

initial import