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5. MATH is a square. ML = 2x + 10, HL 6x-14, find x and HA. = M A T

5. MATH is a square. ML = 2x + 10, HL 6x-14, find x and HA. = M A T

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Solve for the indicated measures

**Solve for the Indicated Measures** **5.** MATH is a square. Given: - \( ML = 2x + 10 \) - \( HL = 6x - 14 \) Find \( x \) and \( HA \). **Diagram Explanation:** The diagram shows square MATH with diagonals MA and HT intersecting at point L. Each side of the square is denoted by the letters M, A, T, and H sequentially. The diagonals are drawn from: - M to A - H to T The intersection of these diagonals occurs at point L, which is the center of the square. **Solution Strategy:** 1. Since MATH is a square, the diagonals are equal and bisect each other. Therefore, \( ML = HL \). 2. Set the equation \( 2x + 10 = 6x - 14 \). 3. Solve for \( x \). 4. Use the value of \( x \) to find \( HA \), knowing that in a square, all sides are equal, and each half of a diagonal is a different expression in terms of \( x \).
Transcribed Image Text:**Solve for the Indicated Measures** **5.** MATH is a square. Given: - \( ML = 2x + 10 \) - \( HL = 6x - 14 \) Find \( x \) and \( HA \). **Diagram Explanation:** The diagram shows square MATH with diagonals MA and HT intersecting at point L. Each side of the square is denoted by the letters M, A, T, and H sequentially. The diagonals are drawn from: - M to A - H to T The intersection of these diagonals occurs at point L, which is the center of the square. **Solution Strategy:** 1. Since MATH is a square, the diagonals are equal and bisect each other. Therefore, \( ML = HL \). 2. Set the equation \( 2x + 10 = 6x - 14 \). 3. Solve for \( x \). 4. Use the value of \( x \) to find \( HA \), knowing that in a square, all sides are equal, and each half of a diagonal is a different expression in terms of \( x \).
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