Answer:
i. The ratio of the areas of the two triangles is 5:8.
ii. The area of the larger triangle is 24 in².
Step-by-step explanation:
Let the area of the smaller triangle be represented by [tex]A_{1}[/tex], and that of the larger triangle by [tex]A_{2}[/tex].
Area of a triangle = [tex]\frac{1}{2}[/tex] x b x h
Where; b is its base and h the height.
Thus,
a. The ratio of the area of the two triangles is:
[tex]\frac{area of the smaller triangle}{area of the larger triangle}[/tex]
Area of smaller triangle = [tex]\frac{1}{2}[/tex] x b x h
= [tex]\frac{1}{2}[/tex] x 5 x h
= [tex]\frac{5}{2}[/tex]h
Area of the lager triangle = [tex]\frac{1}{2}[/tex] x b x h
= [tex]\frac{1}{2}[/tex] x 8 x h
= 4h
So that;
Ratio = [tex]\frac{\frac{5}{2}h }{4h}[/tex]
= [tex]\frac{5}{8}[/tex]
The ratio of the areas of the two triangles is 5:8.
b. If the area of the smaller triangle is 15 in², then the area of the larger triangle can be determined as;
[tex]\frac{area of the smaller triangle}{area of the larger triangle}[/tex] = [tex]\frac{5}{8}[/tex]
[tex]\frac{15}{A_{2} }[/tex] = [tex]\frac{5}{8}[/tex]
5 [tex]A_{2}[/tex] = 15 x 8
= 120
[tex]A_{2}[/tex] = [tex]\frac{120}{5}[/tex]
= 24
The area of the larger triangle is 24 in².
