Problem preview

G-GPE.7 Warmup M1-046-A09-V03

Use coordinate methods to compute polygon perimeters and areas of triangles/rectangles.

Find a missing x-coordinate from the length of a horizontal side

Problem

A right triangle has vertices \((0,0)\), \((a,0)\), \((0,4)\), hypotenuse \(5\), and perimeter \(12\), with no assumed left-right order. Derive the horizontal leg length, write the absolute-value equation, solve for all real \(a\)-values, and check them.

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horizontal leg = 6; equation = |a|=6; solution set = −6,6; check = 6²+4²≠5²

horizontal leg = 12−4−5=3; equation = a=3; solution set = 3; check = 3²+4²=5² for the right-hand placement

horizontal leg = 12-4-5=3; equation = |a|=3; solution set = −3,3; check = 3²+4²=5²

horizontal leg = 12−4−5=3; equation = |a|=3; solution set = −3,7; check = −3 satisfies the equation but 7 does not

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Curriculum context

Course: Math I
Standard: G-GPE.7
Category: Geometry
Domain: Expressing Geometric Properties with Equations
Objective: Use coordinate methods to compute polygon perimeters and areas of triangles/rectangles.
Problem type: Find a missing x-coordinate from the length of a horizontal side