Question

please help me with this question

Answer 1

Answer:

$\text{14. FD = 35}\\\\\text{15. }\angle\text{HIF}=58^\circ$

Step-by-step explanation:

$\text{Solution: }$

$\text{14. HG = }\dfrac{1}{2}\times \text{FD}\hspace{1cm}[\text{The line joining two midpoints in a triangle, HG is }\\\text{}\hspace{3.7cm}\text{ half of the third side, FD.]}\\\text{or, }17.5=\dfrac{1}{2}\times \text{FD}\\\\\text{or, FD = }35$

Or you may solve this using the similar triangles concept as follows:

$\text{14. }\\\\\text{I. EG}=\dfrac{1}{2}\times \text{ED}=\dfrac{1}{2}\times 18.2=9.1$

$\text{II. In triangles EGH and EDF, }\\\text{i. }\angle\text{E}=\angle \text{E}\ \ \ (\text{A})\ \ \ [\text{Common angle.}]\\\text{ii. }\angle \text{EGH}=\angle\text{EDF}\ \ \ \text{(A)}\ \ \ [\text{Corresponding angles.}]\\\text{iii. }\triangle\text{EGH}\sim\triangle\text{EDF}\ \ \ [\text{By A.A. axiom.}]$

$\text{III. }\dfrac{\text{ED}}{\text{EG}}=\dfrac{\text{FD}}{\text{HG}}\ \ \ [\text{Corresponding sides of similar triangles are proportional.}]\\\\\\\text{or, }\dfrac{18.2}{9.1}=\dfrac{\text{FD}}{17.5}\\\\\text{or, }2=\dfrac{\text{FD}}{\text{17.5}}\\\\\text{or, FD = }35$

$\text{15. }\angle \text{HIF}=\angle\text{HIG}=58^\circ\ \ \ [\text{Alternate angles are equal in measure.}]$