Question

Two triangles have bases with lengths 5in and 8in.

Answer 1

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 $A_{1}$, and that of the larger triangle by $A_{2}$.

Area of a triangle = $\frac{1}{2}$ 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:

$\frac{area of the smaller triangle}{area of the larger triangle}$

Area of smaller triangle = $\frac{1}{2}$ x b x h

                                       = $\frac{1}{2}$ x 5 x h

                                       = $\frac{5}{2}$h

Area of the lager triangle = $\frac{1}{2}$ x b x h

                                           = $\frac{1}{2}$ x 8 x h

                                           = 4h

So that;

Ratio = $\frac{\frac{5}{2}h }{4h}$

         = $\frac{5}{8}$

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;

$\frac{area of the smaller triangle}{area of the larger triangle}$ = $\frac{5}{8}$

$\frac{15}{A_{2} }$ = $\frac{5}{8}$

5 $A_{2}$ = 15 x 8

       = 120

$A_{2}$ = $\frac{120}{5}$

    = 24

The area of the larger triangle is 24 in².