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HMMT 十一月 2013 · 冲刺赛 · 第 6 题

HMMT November 2013 — Guts Round — Problem 6

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] A right triangle has area 5 and a hypotenuse of length 5. Find its perimeter.
    HMMT NOVEMBER 2013, 9 NOVEMBER 2013 — GUTS ROUND

英文原题

[ 6 ] A right triangle has area 5 and a hypotenuse of length 5. Find its perimeter.
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HMMT NOVEMBER 2013, 9 NOVEMBER 2013 — GUTS ROUND

解析

英文解析

  1. [ 6 ] A right triangle has area 5 and a hypotenuse of length 5. Find its perimeter.
    √
    √
    2 2
    2 2
    Answer: 5 + 3 5 If x, y denote the legs, then xy = 10 and x + y = 25, so x + y + x + y =
    √
    √ √
    2 2
    ( x + y ) + 2 xy + 5 = 45 + 5 = 5 + 3 5.