Problem preview

A-CED.1 Warmup M2-002-A05-V04

Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.

Create and solve a quadratic equation from an area context

Problem

A triangle has base \(x~\text{units}\), height \(x~+~6~\text{units}\), and area \(40~\text{square}~\text{units}\). Use the displayed dimensions to write and solve the area equation. Report the context-valid root and then the rejected root.

Answer choices

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Equation: ½x(x+2)=40; valid root: x=8; rejected root: x=−10.

Equation: ½x(x+6)=40; valid root: x=−3+√89; rejected root: x=−3−√89.

Equation: x(x+6)=40; valid root: x=4; rejected root: x=−10.

Equation: ½x(x+6)=40; valid root: x=−3−√89; rejected root: x=−3+√89.

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Curriculum context

Course: Math II
Standard: A-CED.1
Category: Algebra
Domain: Creating Equations
Objective: Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.
Problem type: Create and solve a quadratic equation from an area context