Answer:
h = 27.4 in
Step-by-step explanation:
Height = h
Width = h + 7
Diagonal = 44
These 3 form a right-angle triangle, we can therefore use pythagoras theorem to formulate a solveable equation to find h:
h² + (h + 7)² = (44)²
h² + h² + 14h + 49 = 1936
2h² + 14h - 1887 = 0
[tex]2(h^{2} + 7h -\frac{1887}{2}) = 0 \\\\ 2((h + \frac{7}{2})^{2}-\frac{49}{4} -\frac{1887}{2}) = 0 \\\\ 2((h + \frac{7}{2})^{2}-\frac{3823}{4}) = 0 \\\\ 2(h + \frac{7}{2})^{2} - \frac{3823}{2} = 0 \\\\ (h + \frac{7}{2})^{2} = \frac{3823}{4} \\\\ h + \frac{7}{2} = \frac{+}{}\frac{\sqrt{3823}}{2} \\\\ h = -\frac{7}{2} \frac{+}{} \frac{\sqrt{3823}}{2} \\\\ h = 27.4152... \ or \ h = -34.4152...[/tex]
The height cannot be a negative value ∴ the height we are looking for is the other.
h = 27.4 in
